Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
4001	Maximize the Equation given the Constraints	f=3x+22y , 14x+7y=63 , 5x+5y=90	$f = 3 x + 22 y$ , $14 x + 7 y = 63$ , $5 x + 5 y = 90$
4002	Maximize the Equation given the Constraints	f=4x+9y+4z , 4x+7y+9z=110 , 6x+5y+z=175 , x+4y+8z=55	$f = 4 x + 9 y + 4 z$ , $4 x + 7 y + 9 z = 110$ , $6 x + 5 y + z = 175$ , $x + 4 y + 8 z = 55$
4003	Maximize the Equation given the Constraints	f=50x+30y , x+2y=48 , x+y=30 , 2x+y=50	$f = 50 x + 30 y$ , $x + 2 y = 48$ , $x + y = 30$ , $2 x + y = 50$
4004	Maximize the Equation given the Constraints	f=7x+10y+4z , 3x+5y+4z=30 , 3x+2y=4 , x+2y=8	$f = 7 x + 10 y + 4 z$ , $3 x + 5 y + 4 z = 30$ , $3 x + 2 y = 4$ , $x + 2 y = 8$
4005	Maximize the Equation given the Constraints	2x+y=20 , 10x+y=36 , 2x+5y=36 , z=3x+4y	$2 x + y = 20$ , $10 x + y = 36$ , $2 x + 5 y = 36$ , $z = 3 x + 4 y$
4006	Maximize the Equation given the Constraints	30x+10y=360 , 10x+10y=160 , 10x+30y=240 , x , y=0 , c=8x+4y	$30 x + 10 y = 360$ , $10 x + 10 y = 160$ , $10 x + 30 y = 240$ , $x$ , $y = 0$ , $c = 8 x + 4 y$
4007	Maximize the Equation given the Constraints	3a+2b+4c=1d , 1a+7b+5c=34 , 2a+0+6c=76 , 8b+9c+1d=41 , a=0 , b=0 , c=0	$3 a + 2 b + 4 c = 1 d$ , $1 a + 7 b + 5 c = 34$ , $2 a + 0 + 6 c = 76$ , $8 b + 9 c + 1 d = 41$ , $a = 0$ , $b = 0$ , $c = 0$
4008	Maximize the Equation given the Constraints	3x+8y=35 , 6x+4y=40 , x=0 , y=0 , p=2x+3y	$3 x + 8 y = 35$ , $6 x + 4 y = 40$ , $x = 0$ , $y = 0$ , $p = 2 x + 3 y$
4009	Maximize the Equation given the Constraints	4x-y=15 , 3x+y=14 , x=2 , y=9 , z=4x+4y	$4 x - y = 15$ , $3 x + y = 14$ , $x = 2$ , $y = 9$ , $z = 4 x + 4 y$
4010	Maximize the Equation given the Constraints	4x-y=16 , 2x+y=11	$4 x - y = 16$ , $2 x + y = 11$
4011	Maximize the Equation given the Constraints	4y1+4y2=16 , 4y1+y2=20 , w=6y1+y2	$4 y \cdot 1 + 4 y \cdot 2 = 16$ , $4 y \cdot 1 + y \cdot 2 = 20$ , $w = 6 y \cdot 1 + y \cdot 2$
4012	Maximize the Equation given the Constraints	64x+128y=10240 , 1x+0.5y=91 , 12x+12y=2000	$64 x + 128 y = 10240$ , $1 x + 0.5 y = 91$ , $12 x + 12 y = 2000$
4013	Maximize the Equation given the Constraints	6x+2y=18000 , 3x+4y=12000 , 0.25x+0.16y=z	$6 x + 2 y = 18000$ , $3 x + 4 y = 12000$ , $0.25 x + 0.16 y = z$
4014	Maximize the Equation given the Constraints	6x+2y>12 , 5x-3y<15 , y=1	$6 x + 2 y > 12$ , $5 x - 3 y < 15$ , $y = 1$
4015	Maximize the Equation given the Constraints	75v+100w+150x+150y+250z=2700 , 40w+80x+90y+120z=900 , 15v+20w+40x=180 , 30y+45z=180 , 20v+32w+60x+35y+55z=a	$75 v + 100 w + 150 x + 150 y + 250 z = 2700$ , $40 w + 80 x + 90 y + 120 z = 900$ , $15 v + 20 w + 40 x = 180$ , $30 y + 45 z = 180$ , $20 v + 32 w + 60 x + 35 y + 55 z = a$
4016	Maximize the Equation given the Constraints	7x-10y=0 , 10x-7y=0 , p=3x+y , x+y=17	$7 x - 10 y = 0$ , $10 x - 7 y = 0$ , $p = 3 x + y$ , $x + y = 17$
4017	Solve Using a Matrix with Cramer's Rule	x+y-z=11 , 3x-y+z=-3 , x-4y+2z=-54	$x + y - z = 11$ , $3 x - y + z = - 3$ , $x - 4 y + 2 z = - 54$
4018	Solve Using a Matrix with Cramer's Rule	x+y-z=7 , 4x-y+z=-17 , x-3y+2z=-40	$x + y - z = 7$ , $4 x - y + z = - 17$ , $x - 3 y + 2 z = - 40$
4019	Solve Using a Matrix with Cramer's Rule	x=7(y-5) , 4y=3x+5	$x = 7 (y - 5)$ , $4 y = 3 x + 5$
4020	Solve Using a Matrix with Cramer's Rule	x-14y+z-2w=1 , 7x+7y+z+3w=2 , 8x-7y+2z+w=3	$x - 14 y + z - 2 w = 1$ , $7 x + 7 y + z + 3 w = 2$ , $8 x - 7 y + 2 z + w = 3$
4021	Solve Using a Matrix with Cramer's Rule	x-2y+z=-2 , -2x+4y+6z=-5 , -5x-3y+z=-4	$x - 2 y + z = - 2$ , $- 2 x + 4 y + 6 z = - 5$ , $- 5 x - 3 y + z = - 4$
4022	Solve Using a Matrix with Cramer's Rule	x-2y=0 , x+y+z=310 , 45000x+40000y+80000z=16000000	$x - 2 y = 0$ , $x + y + z = 310$ , $45000 x + 40000 y + 80000 z = 16000000$
4023	Solve Using a Matrix with Cramer's Rule	x-2y=0 , x+y+z=320 , 25000x+50000y+80000z=13000000	$x - 2 y = 0$ , $x + y + z = 320$ , $25000 x + 50000 y + 80000 z = 13000000$
4024	Solve Using a Matrix with Cramer's Rule	x-2y=0 , x+y+z=320 , 25000x+80000y+70000z=16000000	$x - 2 y = 0$ , $x + y + z = 320$ , $25000 x + 80000 y + 70000 z = 16000000$
4025	Solve Using a Matrix with Cramer's Rule	-x-2y=12 , 2x+4y=-24	$- x - 2 y = 12$ , $2 x + 4 y = - 24$
4026	Solve Using a Matrix with Cramer's Rule	x-2y=-2 , 2x+y=6	$x - 2 y = - 2$ , $2 x + y = 6$
4027	Solve Using a Matrix with Cramer's Rule	x-3y+4z=25 , y-z+w=-12 , -2x+3y-3z+3w=-18 , 3y-4z+w=-29	$x - 3 y + 4 z = 25$ , $y - z + w = - 12$ , $- 2 x + 3 y - 3 z + 3 w = - 18$ , $3 y - 4 z + w = - 29$
4028	Solve Using a Matrix with Cramer's Rule	x-8y=-21 , -4x+2y=-18	$x - 8 y = - 21$ , $- 4 x + 2 y = - 18$
4029	Solve Using a Matrix with Cramer's Rule	x-y+12z=8 , y-14z=-13 , z=2	$x - y + 12 z = 8$ , $y - 14 z = - 13$ , $z = 2$
4030	Solve Using a Matrix with Cramer's Rule	x-y+3z=0 , 2x+y+2z=-2 , -2x-2y+z=7	$x - y + 3 z = 0$ , $2 x + y + 2 z = - 2$ , $- 2 x - 2 y + z = 7$
4031	Solve Using a Matrix with Cramer's Rule	x-y+z=0 , 2x-z=-1 , -3x-4y=6	$x - y + z = 0$ , $2 x - z = - 1$ , $- 3 x - 4 y = 6$
4032	Solve Using a Matrix with Cramer's Rule	x-y+z=0 , 2y-z=1 , -7x-8y=-4	$x - y + z = 0$ , $2 y - z = 1$ , $- 7 x - 8 y = - 4$
4033	Solve Using a Matrix with Cramer's Rule	x-y=3 , 2x-y=3	$x - y = 3$ , $2 x - y = 3$
4034	Solve Using a Matrix with Cramer's Rule	x-y=5 , 3x-8y=5	$x - y = 5$ , $3 x - 8 y = 5$
4035	Solve Using a Matrix with Cramer's Rule	x-z=0 , x+y+z=94 , 77x+54y+66z=5811	$x - z = 0$ , $x + y + z = 94$ , $77 x + 54 y + 66 z = 5811$
4036	Solve Using a Matrix with Cramer's Rule	y+4z=-2 , x+2y+6z=-7	$y + 4 z = - 2$ , $x + 2 y + 6 z = - 7$
4037	Solve Using a Matrix with Cramer's Rule	y=3x-2 , y=-x+2	$y = 3 x - 2$ , $y = - x + 2$
4038	Solve Using a Matrix with Cramer's Rule	y=4x+3x-2 , y=5x	$y = 4 x + 3 x - 2$ , $y = 5 x$
4039	Solve Using a Matrix with Cramer's Rule	y=x-3 , y=1+z , z=4-x	$y = x - 3$ , $y = 1 + z$ , $z = 4 - x$
4040	Maximize the Equation given the Constraints	p=5x+8y+7z , x+y+z=6 , 5x+5y+3z=22	$p = 5 x + 8 y + 7 z$ , $x + y + z = 6$ , $5 x + 5 y + 3 z = 22$
4041	Maximize the Equation given the Constraints	p=5x+8y+7z , x+y+z=6 , 5x+5y+3z=22 , x=0 , y=0 , z=0 , p=28	$p = 5 x + 8 y + 7 z$ , $x + y + z = 6$ , $5 x + 5 y + 3 z = 22$ , $x = 0$ , $y = 0$ , $z = 0$ , $p = 28$
4042	Maximize the Equation given the Constraints	p=5x-4y+3z , 10x+10z=100 , 5y-5z=50 , 10x-5y=50 , x=0 , y=0 , z=0	$p = 5 x - 4 y + 3 z$ , $10 x + 10 z = 100$ , $5 y - 5 z = 50$ , $10 x - 5 y = 50$ , $x = 0$ , $y = 0$ , $z = 0$
4043	Maximize the Equation given the Constraints	p=6x+8y+4z , 3x+y+z=5 , x+2y+z=5 , x+y+z=4 , x=0 , y=0 , z=0	$p = 6 x + 8 y + 4 z$ , $3 x + y + z = 5$ , $x + 2 y + z = 5$ , $x + y + z = 4$ , $x = 0$ , $y = 0$ , $z = 0$
4044	Maximize the Equation given the Constraints	p=8x+8y , 2x+y=10 , x+2y=8	$p = 8 x + 8 y$ , $2 x + y = 10$ , $x + 2 y = 8$
4045	Maximize the Equation given the Constraints	p=x , x-y=4 , -x+3y=4 , x=0	$p = x$ , $x - y = 4$ , $- x + 3 y = 4$ , $x = 0$
4046	Maximize the Equation given the Constraints	p=x+3y , x+y=4 , 3x+y=5 , x=0 , y=0	$p = x + 3 y$ , $x + y = 4$ , $3 x + y = 5$ , $x = 0$ , $y = 0$
4047	Maximize the Equation given the Constraints	w=2y1+y2+2y3 , y1+y2+y3=12 , 3y1+y2=40	$w = 2 y \cdot 1 + y \cdot 2 + 2 y \cdot 3$ , $y \cdot 1 + y \cdot 2 + y \cdot 3 = 12$ , $3 y \cdot 1 + y \cdot 2 = 40$
4048	Maximize the Equation given the Constraints	w=y1+3y2+6y3 , 4y1+5y2+7y3=-3	$w = y \cdot 1 + 3 y \cdot 2 + 6 y \cdot 3$ , $4 y \cdot 1 + 5 y \cdot 2 + 7 y \cdot 3 = - 3$
4049	Maximize the Equation given the Constraints	x+3y , x+y=7 , x+2y=10 , x=0 , y=0	$x + 3 y$ , $x + y = 7$ , $x + 2 y = 10$ , $x = 0$ , $y = 0$
4050	Maximize the Equation given the Constraints	x+4y<4 , 0<4 , x+4y=4	$x + 4 y < 4$ , $0 < 4$ , $x + 4 y = 4$
4051	Maximize the Equation given the Constraints	x=12x+10y , 15x+10y=1380 , 10x+12y=1320	$x = 12 x + 10 y$ , $15 x + 10 y = 1380$ , $10 x + 12 y = 1320$
4052	Maximize the Equation given the Constraints	x=12x+10y , 15x+10y=1380 , 10x+12y=1320 , x=0 , y=0	$x = 12 x + 10 y$ , $15 x + 10 y = 1380$ , $10 x + 12 y = 1320$ , $x = 0$ , $y = 0$
4053	Maximize the Equation given the Constraints	x-y=-4 , 3x+2y=18 , z=3x+9y	$x - y = - 4$ , $3 x + 2 y = 18$ , $z = 3 x + 9 y$
4054	Maximize the Equation given the Constraints	y-3<5 , y=9	$y - 3 < 5$ , $y = 9$
4055	Maximize the Equation given the Constraints	z=0.039x+0.029y , 2.40x+0.08y=144 , x+y=100 , x=60 , y=70 , x=0 , x=0	$z = 0.039 x + 0.029 y$ , $2.4 x + 0.08 y = 144$ , $x + y = 100$ , $x = 60$ , $y = 70$ , $x = 0$ , $x = 0$
4056	Maximize the Equation given the Constraints	z=0.07x+0.09y , 0.5x+y=40000000 , x+y=45000000 , x=5000000 , y=15000000	$z = 0.07 x + 0.09 y$ , $0.5 x + y = 40000000$ , $x + y = 45000000$ , $x = 5000000$ , $y = 15000000$
4057	Maximize the Equation given the Constraints	z=10x+10y , 13x-15y=12 , x+y=44 , x , y=0	$z = 10 x + 10 y$ , $13 x - 15 y = 12$ , $x + y = 44$ , $x$ , $y = 0$
4058	Maximize the Equation given the Constraints	z=10x+10y , 15x-15y=45 , x+y=45 , x=0 , y=0	$z = 10 x + 10 y$ , $15 x - 15 y = 45$ , $x + y = 45$ , $x = 0$ , $y = 0$
4059	Maximize the Equation given the Constraints	z=10x+10y , 5x+6y=75 , 15x-13y=70 , x+y=42 , x , y=0	$z = 10 x + 10 y$ , $5 x + 6 y = 75$ , $15 x - 13 y = 70$ , $x + y = 42$ , $x$ , $y = 0$
4060	Maximize the Equation given the Constraints	z=10x+10y , 6x+8y=108 , 16x-13y=82 , x+y=45 , x , y=0	$z = 10 x + 10 y$ , $6 x + 8 y = 108$ , $16 x - 13 y = 82$ , $x + y = 45$ , $x$ , $y = 0$
4061	Maximize the Equation given the Constraints	z=10x+10y , 7x+6y=105 , 18x-11y=85 , x+y=45 , x , y=0	$z = 10 x + 10 y$ , $7 x + 6 y = 105$ , $18 x - 11 y = 85$ , $x + y = 45$ , $x$ , $y = 0$
4062	Maximize the Equation given the Constraints	z=10x+10y , 7x+8y=119 , 14x-15y=21 , x+y=45	$z = 10 x + 10 y$ , $7 x + 8 y = 119$ , $14 x - 15 y = 21$ , $x + y = 45$
4063	Maximize the Equation given the Constraints	z=10x+19y , 4x+2y=24 , 4x+4y=28	$z = 10 x + 19 y$ , $4 x + 2 y = 24$ , $4 x + 4 y = 28$
4064	Maximize the Equation given the Constraints	z=12x+14y , -2x+y=6 , x+y=15 , 3x-y=0 , x , y=0	$z = 12 x + 14 y$ , $- 2 x + y = 6$ , $x + y = 15$ , $3 x - y = 0$ , $x$ , $y = 0$
4065	Maximize the Equation given the Constraints	z=13x+6 , x+y=21000 , x+y=6000	$z = 13 x + 6$ , $x + y = 21000$ , $x + y = 6000$
4066	Maximize the Equation given the Constraints	z=15+7y , 8x+3y=24 , 10x+y=24	$z = 15 + 7 y$ , $8 x + 3 y = 24$ , $10 x + y = 24$
4067	Maximize the Equation given the Constraints	z=15x+15y , 6x+6y=114 , 15x-9y=141 , x+y=43 , x , y=0	$z = 15 x + 15 y$ , $6 x + 6 y = 114$ , $15 x - 9 y = 141$ , $x + y = 43$ , $x$ , $y = 0$
4068	Maximize the Equation given the Constraints	z=15x+15y , 7x+10y=133 , 15x-12y=51 , x+y=43 , x , y=0	$z = 15 x + 15 y$ , $7 x + 10 y = 133$ , $15 x - 12 y = 51$ , $x + y = 43$ , $x$ , $y = 0$
4069	Maximize the Equation given the Constraints	z=15x+15y , 7x+7y=42 , 15x-11y=36 , x+y=42 , x , y=0	$z = 15 x + 15 y$ , $7 x + 7 y = 42$ , $15 x - 11 y = 36$ , $x + y = 42$ , $x$ , $y = 0$
4070	Maximize the Equation given the Constraints	z=15x+15y , 9x+6y=135 , 11x-15y=-36 , x+y=44 , x , y=0	$z = 15 x + 15 y$ , $9 x + 6 y = 135$ , $11 x - 15 y = - 36$ , $x + y = 44$ , $x$ , $y = 0$
4071	Maximize the Equation given the Constraints	z=15x+6y , 4x+3y=20 , 4x+8y=32 , x=0 , y=0	$z = 15 x + 6 y$ , $4 x + 3 y = 20$ , $4 x + 8 y = 32$ , $x = 0$ , $y = 0$
4072	Maximize the Equation given the Constraints	z=2.996x+3.98y , 52x+2.15y=50.5 , 22.25y=41.5 , 260x+102.7y=485 , 150x=550 , x=0 , y=0	$z = 2.996 x + 3.98 y$ , $52 x + 2.15 y = 50.5$ , $22.25 y = 41.5$ , $260 x + 102.7 y = 485$ , $150 x = 550$ , $x = 0$ , $y = 0$
4073	Maximize the Equation given the Constraints	z=20x+16y , 4x+3y=12 , -2x+4y=16 , 6x-y=18 , x=0 , y=0	$z = 20 x + 16 y$ , $4 x + 3 y = 12$ , $- 2 x + 4 y = 16$ , $6 x - y = 18$ , $x = 0$ , $y = 0$
4074	Maximize the Equation given the Constraints	z=22x+2y , 4x+8y=32 , 11x+y=32	$z = 22 x + 2 y$ , $4 x + 8 y = 32$ , $11 x + y = 32$
4075	Maximize the Equation given the Constraints	z=25x+40y , 10000x+15000y=300000 , 180000x+120000y=3600000 , x=0 , y=0	$z = 25 x + 40 y$ , $10000 x + 15000 y = 300000$ , $180000 x + 120000 y = 3600000$ , $x = 0$ , $y = 0$
4076	Maximize the Equation given the Constraints	z=2x1+3x2 , 5x1+x2=40 , 3x1+2x2=60 , x1+x2=50 , x1=0 , x2=0	$z = 2 x \cdot 1 + 3 x \cdot 2$ , $5 x \cdot 1 + x \cdot 2 = 40$ , $3 x \cdot 1 + 2 x \cdot 2 = 60$ , $x \cdot 1 + x \cdot 2 = 50$ , $x \cdot 1 = 0$ , $x \cdot 2 = 0$
4077	Maximize the Equation given the Constraints	z=2x1+8x2 , x1+9x2=15 , 8x1+5x2=25 , x=0 , y=0	$z = 2 x \cdot 1 + 8 x \cdot 2$ , $x \cdot 1 + 9 x \cdot 2 = 15$ , $8 x \cdot 1 + 5 x \cdot 2 = 25$ , $x = 0$ , $y = 0$
4078	Maximize the Equation given the Constraints	z=2x1+9x2 , 5x1+x2=40 , 9x1+2x2=60 , x1+x2=50 , x*1=0	$z = 2 x \cdot 1 + 9 x \cdot 2$ , $5 x \cdot 1 + x \cdot 2 = 40$ , $9 x \cdot 1 + 2 x \cdot 2 = 60$ , $x \cdot 1 + x \cdot 2 = 50$ , $x \cdot 1 = 0$
4079	Maximize the Equation given the Constraints	z=2x1+x2 , x1+3x2=12 , 2x1+2x2=6 , x1+4x2=4 , x1=0 , x2=0	$z = 2 x \cdot 1 + x \cdot 2$ , $x \cdot 1 + 3 x \cdot 2 = 12$ , $2 x \cdot 1 + 2 x \cdot 2 = 6$ , $x \cdot 1 + 4 x \cdot 2 = 4$ , $x \cdot 1 = 0$ , $x \cdot 2 = 0$
4080	Maximize the Equation given the Constraints	z=2x+3y , 2x+y=10 , x+2y=8 , x , y=0	$z = 2 x + 3 y$ , $2 x + y = 10$ , $x + 2 y = 8$ , $x$ , $y = 0$
4081	Maximize the Equation given the Constraints	z=2x+7y , 5x+4y=20 , 8x+y=20	$z = 2 x + 7 y$ , $5 x + 4 y = 20$ , $8 x + y = 20$
4082	Maximize the Equation given the Constraints	z=2x+8y , x+9y=15 , 8x+5y=25	$z = 2 x + 8 y$ , $x + 9 y = 15$ , $8 x + 5 y = 25$
4083	Maximize the Equation given the Constraints	z=2x+y , x=2 , y=1 , 2x-y=-1	$z = 2 x + y$ , $x = 2$ , $y = 1$ , $2 x - y = - 1$
4084	Maximize the Equation given the Constraints	z=2x=11y , 6x+7y=42 , 12x+y=0	$z = 2 x = 11 y$ , $6 x + 7 y = 42$ , $12 x + y = 0$
4085	Maximize the Equation given the Constraints	z=33x+15y , 5x+7y=35 , 11x+y=35 , x=0 , y=0	$z = 33 x + 15 y$ , $5 x + 7 y = 35$ , $11 x + y = 35$ , $x = 0$ , $y = 0$
4086	Maximize the Equation given the Constraints	z=35a+50b , a+b=140 , 10a+b=150 , a=95 , b=108	$z = 35 a + 50 b$ , $a + b = 140$ , $10 a + b = 150$ , $a = 95$ , $b = 108$
4087	Maximize the Equation given the Constraints	z=35x+40y , x+y=120 , 20x+10y=1500 , x=45 , y=32	$z = 35 x + 40 y$ , $x + y = 120$ , $20 x + 10 y = 1500$ , $x = 45$ , $y = 32$
4088	Maximize the Equation given the Constraints	z=3x+5y , 2x-3y=12 , x+y=4 , 3x+4y=36 , x=0 , y=0	$z = 3 x + 5 y$ , $2 x - 3 y = 12$ , $x + y = 4$ , $3 x + 4 y = 36$ , $x = 0$ , $y = 0$
4089	Find the Intersection of the Inequalities	x-y<1 , 2x+3y=12	$x - y < 1$ , $2 x + 3 y = 12$
4090	Find the Intersection of the Inequalities	x-y=1 , 3x+2y=18 , x=0 , y=0	$x - y = 1$ , $3 x + 2 y = 18$ , $x = 0$ , $y = 0$
4091	Find the Intersection of the Inequalities	x-y=3 , 3x+2y=24	$x - y = 3$ , $3 x + 2 y = 24$
4092	Find the Intersection of the Inequalities	-x-y=5 , 2x-y=4	$- x - y = 5$ , $2 x - y = 4$
4093	Find the Intersection of the Inequalities	y<1/2x-2 , y>-2x-1	$y < \frac{1}{2} x - 2$ , $y > - 2 x - 1$
4094	Find the Intersection of the Inequalities	y=3x-4 , y=-2x-1	$y = 3 x - 4$ , $y = - 2 x - 1$
4095	Find the Intersection of the Inequalities	y=5x , x=4y	$y = 5 x$ , $x = 4 y$
4096	Find the Intersection of the Inequalities	y>2x+4 , 2x-y=4	$y > 2 x + 4$ , $2 x - y = 4$
4097	Find the Intersection of the Inequalities	y>-x-3 , y>2x	$y > - x - 3$ , $y > 2 x$
4098	Find the Union of the Inequalities	0.09x+0.006y=15.2 , x+y=560	$0.09 x + 0.006 y = 15.2$ , $x + y = 560$
4099	Find the Union of the Inequalities	0.5x+y=350000000 , x+y=40000000 , x=5000000 , y=10000000	$0.5 x + y = 350000000$ , $x + y = 40000000$ , $x = 5000000$ , $y = 10000000$
4100	Find the Union of the Inequalities	(x-1)^2+(y+1)^2<36 , (x-1)^2+(y+1)^2=4	${(x - 1)}^{2} + {(y + 1)}^{2} < 36$ , ${(x - 1)}^{2} + {(y + 1)}^{2} = 4$