Algebra Examples

$[\begin{array}{c} 10 & 5 \\ 16 & 10.5 \end{array}] = [\begin{array}{c} 4 x - 6 & 8 - 10 x \\ 4 x & 15 t + 1.5 t \end{array}]$

Step 1

Add $15 t$ and $1.5 t$ .

$[\begin{array}{c} 10 & 5 \\ 16 & 10.5 \end{array}] = [\begin{array}{c} 4 x - 6 & 8 - 10 x \\ 4 x & 16.5 t \end{array}]$

Step 2

Write as a linear system of equations.

$10 = 4 x - 6$

$5 = 8 - 10 x$

$16 = 4 x$

$10.5 = 16.5 t$

Step 3

Solve the system of equations.

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Step 3.1

Solve for $x$ in $10 = 4 x - 6$ .

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Step 3.1.1

Rewrite the equation as $4 x - 6 = 10$ .

$4 x - 6 = 10$

$5 = 8 - 10 x$

$16 = 4 x$

$10.5 = 16.5 t$

Step 3.1.2

Move all terms not containing $x$ to the right side of the equation.

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Step 3.1.2.1

Add $6$ to both sides of the equation.

$4 x = 10 + 6$

$5 = 8 - 10 x$

$16 = 4 x$

$10.5 = 16.5 t$

Step 3.1.2.2

Add $10$ and $6$ .

$4 x = 16$

$5 = 8 - 10 x$

$16 = 4 x$

$10.5 = 16.5 t$

$4 x = 16$

$5 = 8 - 10 x$

$16 = 4 x$

$10.5 = 16.5 t$

Step 3.1.3

Divide each term in $4 x = 16$ by $4$ and simplify.

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Step 3.1.3.1

Divide each term in $4 x = 16$ by $4$ .

$\frac{4 x}{4} = \frac{16}{4}$

$5 = 8 - 10 x$

$16 = 4 x$

$10.5 = 16.5 t$

Step 3.1.3.2

Simplify the left side.

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Step 3.1.3.2.1

Cancel the common factor of $4$ .

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Step 3.1.3.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{16}{4}$

$5 = 8 - 10 x$

$16 = 4 x$

$10.5 = 16.5 t$

Step 3.1.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{16}{4}$

$5 = 8 - 10 x$

$16 = 4 x$

$10.5 = 16.5 t$

$x = \frac{16}{4}$

$5 = 8 - 10 x$

$16 = 4 x$

$10.5 = 16.5 t$

$x = \frac{16}{4}$

$5 = 8 - 10 x$

$16 = 4 x$

$10.5 = 16.5 t$

Step 3.1.3.3

Simplify the right side.

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Step 3.1.3.3.1

Divide $16$ by $4$ .

$x = 4$

$5 = 8 - 10 x$

$16 = 4 x$

$10.5 = 16.5 t$

$x = 4$

$5 = 8 - 10 x$

$16 = 4 x$

$10.5 = 16.5 t$

$x = 4$

$5 = 8 - 10 x$

$16 = 4 x$

$10.5 = 16.5 t$

$x = 4$

$5 = 8 - 10 x$

$16 = 4 x$

$10.5 = 16.5 t$

Step 3.2

Replace all occurrences of $x$ with $4$ in each equation.

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Step 3.2.1

Replace all occurrences of $x$ in $5 = 8 - 10 x$ with $4$ .

$5 = 8 - 10 \cdot 4$

$x = 4$

$16 = 4 x$

$10.5 = 16.5 t$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Simplify $8 - 10 \cdot 4$ .

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Step 3.2.2.1.1

Multiply $- 10$ by $4$ .

$5 = 8 - 40$

$x = 4$

$16 = 4 x$

$10.5 = 16.5 t$

Step 3.2.2.1.2

Subtract $40$ from $8$ .

$5 = - 32$

$x = 4$

$16 = 4 x$

$10.5 = 16.5 t$

$5 = - 32$

$x = 4$

$16 = 4 x$

$10.5 = 16.5 t$

$5 = - 32$

$x = 4$

$16 = 4 x$

$10.5 = 16.5 t$

Step 3.2.3

Replace all occurrences of $x$ in $16 = 4 x$ with $4$ .

$16 = 4 (4)$

$5 = - 32$

$x = 4$

$10.5 = 16.5 t$

Step 3.2.4

Simplify the right side.

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Step 3.2.4.1

Multiply $4$ by $4$ .

$16 = 16$

$5 = - 32$

$x = 4$

$10.5 = 16.5 t$

$16 = 16$

$5 = - 32$

$x = 4$

$10.5 = 16.5 t$

Step 3.2.5

Rewrite the equation as $16.5 t = 10.5$ .

$16.5 t = 10.5$

$16 = 16$

$5 = - 32$

$x = 4$

Step 3.2.6

Divide each term in $16.5 t = 10.5$ by $16.5$ and simplify.

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Step 3.2.6.1

Divide each term in $16.5 t = 10.5$ by $16.5$ .

$\frac{16.5 t}{16.5} = \frac{10.5}{16.5}$

$16 = 16$

$5 = - 32$

$x = 4$

Step 3.2.6.2

Simplify the left side.

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Step 3.2.6.2.1

Cancel the common factor of $16.5$ .

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Step 3.2.6.2.1.1

Cancel the common factor.

$\frac{16.5 t}{16.5} = \frac{10.5}{16.5}$

$16 = 16$

$5 = - 32$

$x = 4$

Step 3.2.6.2.1.2

Divide $t$ by $1$ .

$t = \frac{10.5}{16.5}$

$16 = 16$

$5 = - 32$

$x = 4$

$t = \frac{10.5}{16.5}$

$16 = 16$

$5 = - 32$

$x = 4$

$t = \frac{10.5}{16.5}$

$16 = 16$

$5 = - 32$

$x = 4$

Step 3.2.6.3

Simplify the right side.

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Step 3.2.6.3.1

Divide $10.5$ by $16.5$ .

$t = 0.\overline{63}$

$16 = 16$

$5 = - 32$

$x = 4$

$t = 0.\overline{63}$

$16 = 16$

$5 = - 32$

$x = 4$

$t = 0.\overline{63}$

$16 = 16$

$5 = - 32$

$x = 4$

$t = 0.\overline{63}$

$16 = 16$

$5 = - 32$

$x = 4$

Step 3.3

Since $5 = - 32$ is not true, there is no solution.

$No solution$