Algebra Examples

$x - 2 y = 4$ $y = \frac{1}{2} x + 6$

Step 1

Solve the system of equations.

Tap for more steps...

Step 1.1

Multiply each term in $y = \frac{1}{2} x + 6$ by $2$ to eliminate the fractions.

Tap for more steps...

Step 1.1.1

Multiply each term in $y = \frac{1}{2} x + 6$ by $2$ .

$y \cdot 2 = \frac{1}{2} x \cdot 2 + 6 \cdot 2$

$x - 2 y = 4$

Step 1.1.2

Simplify the left side.

Tap for more steps...

Step 1.1.2.1

Move $2$ to the left of $y$ .

$2 y = \frac{1}{2} x \cdot 2 + 6 \cdot 2$

$x - 2 y = 4$

$2 y = \frac{1}{2} x \cdot 2 + 6 \cdot 2$

$x - 2 y = 4$

Step 1.1.3

Simplify the right side.

Tap for more steps...

Step 1.1.3.1

Simplify each term.

Tap for more steps...

Step 1.1.3.1.1

Combine $\frac{1}{2}$ and $x$ .

$2 y = \frac{x}{2} \cdot 2 + 6 \cdot 2$

$x - 2 y = 4$

Step 1.1.3.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.1.3.1.2.1

Cancel the common factor.

$2 y = \frac{x}{2} \cdot 2 + 6 \cdot 2$

$x - 2 y = 4$

Step 1.1.3.1.2.2

Rewrite the expression.

$2 y = x + 6 \cdot 2$

$x - 2 y = 4$

$2 y = x + 6 \cdot 2$

$x - 2 y = 4$

Step 1.1.3.1.3

Multiply $6$ by $2$ .

$2 y = x + 12$

$x - 2 y = 4$

$2 y = x + 12$

$x - 2 y = 4$

$2 y = x + 12$

$x - 2 y = 4$

$2 y = x + 12$

$x - 2 y = 4$

Step 1.2

Subtract $x$ from both sides of the equation.

$x - 2 y = 4, 2 y - x = 12$

Step 1.3

Reorder the polynomial.

$- x + 2 y = 12$

$x - 2 y = 4$

Step 1.4

Add the two equations together to eliminate $x$ from the system.

		$x$	$-$	$2$	$y$	$=$		$4$
$+$	$-$	$x$	$+$	$2$	$y$	$=$	$1$	$2$
					$0$	$=$	$1$	$6$

Step 1.5

Since $0 \neq 16$ , there are no solutions.

No solution

Step 2

Since the system has no solution, the equations and graphs are parallel and do not intersect. Thus, the system is inconsistent.

Inconsistent

Step 3