Solve by Addition/Elimination 4x+3y=8 and x-2y=-13

$4 x + 3 y = 8$ and $x - 2 y = - 13$

Step 1

Multiply each equation by the value that makes the coefficients of $x$ opposite.

$4 x + 3 y = 8$

$(- 4) \cdot (x - 2 y) = (- 4) (- 13)$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 4) \cdot (x - 2 y)$ .

Apply the distributive property.

$4 x + 3 y = 8$

$- 4 x - 4 (- 2 y) = (- 4) (- 13)$

Multiply $- 2$ by $- 4$ .

$4 x + 3 y = 8$

$- 4 x + 8 y = (- 4) (- 13)$

$4 x + 3 y = 8$

$- 4 x + 8 y = (- 4) (- 13)$

$4 x + 3 y = 8$

$- 4 x + 8 y = (- 4) (- 13)$

Simplify the right side.

Multiply $- 4$ by $- 13$ .

$4 x + 3 y = 8$

$- 4 x + 8 y = 52$

$4 x + 3 y = 8$

$- 4 x + 8 y = 52$

$4 x + 3 y = 8$

$- 4 x + 8 y = 52$

Step 3

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

		$4$	$x$	$+$	$3$	$y$	$=$		$8$
$+$	$-$	$4$	$x$	$+$	$8$	$y$	$=$	$5$	$2$
				$1$	$1$	$y$	$=$	$6$	$0$

Step 4

Divide each term in $11 y = 60$ by $11$ and simplify.

Divide each term in $11 y = 60$ by $11$ .

$\frac{11 y}{11} = \frac{60}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 y}{11} = \frac{60}{11}$

Divide $y$ by $1$ .

$y = \frac{60}{11}$

Step 5

Substitute the value found for $y$ into one of the original equations, then solve for $x$ .

Substitute the value found for $y$ into one of the original equations to solve for $x$ .

$4 x + 3 (\frac{60}{11}) = 8$

Multiply $3 (\frac{60}{11})$ .

Combine $3$ and $\frac{60}{11}$ .

$4 x + \frac{3 \cdot 60}{11} = 8$

Multiply $3$ by $60$ .

$4 x + \frac{180}{11} = 8$

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

Subtract $\frac{180}{11}$ from both sides of the equation.

$4 x = 8 - \frac{180}{11}$

To write $8$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$4 x = 8 \cdot \frac{11}{11} - \frac{180}{11}$

Combine $8$ and $\frac{11}{11}$ .

$4 x = \frac{8 \cdot 11}{11} - \frac{180}{11}$

Combine the numerators over the common denominator.

$4 x = \frac{8 \cdot 11 - 180}{11}$

Simplify the numerator.

Multiply $8$ by $11$ .

$4 x = \frac{88 - 180}{11}$

Subtract $180$ from $88$ .

$4 x = \frac{- 92}{11}$

Move the negative in front of the fraction.

$4 x = - \frac{92}{11}$

Divide each term in $4 x = - \frac{92}{11}$ by $4$ and simplify.

Divide each term in $4 x = - \frac{92}{11}$ by $4$ .

$\frac{4 x}{4} = \frac{- \frac{92}{11}}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- \frac{92}{11}}{4}$

Divide $x$ by $1$ .

$x = \frac{- \frac{92}{11}}{4}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{92}{11} \cdot \frac{1}{4}$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{92}{11}$ into the numerator.

$x = \frac{- 92}{11} \cdot \frac{1}{4}$

Factor $4$ out of $- 92$ .

$x = \frac{4 (- 23)}{11} \cdot \frac{1}{4}$

Cancel the common factor.

$x = \frac{4 \cdot - 23}{11} \cdot \frac{1}{4}$

Rewrite the expression.

$x = \frac{- 23}{11}$

Move the negative in front of the fraction.

$x = - \frac{23}{11}$

Step 6

The solution to the independent system of equations can be represented as a point.

$(- \frac{23}{11}, \frac{60}{11})$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- \frac{23}{11}, \frac{60}{11})$

Equation Form:

$x = - \frac{23}{11}, y = \frac{60}{11}$

Step 8

Solve by Addition/Elimination 4x+3y=8 and x-2y=-13

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