Solve by Addition/Elimination 4x+2y=6 4x-5y=-1

$4 x + 2 y = 6$ $4 x - 5 y = - 1$

Step 1

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

$(- 1) \cdot (4 x + 2 y) = (- 1) (6)$

$4 x - 5 y = - 1$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (4 x + 2 y)$ .

Apply the distributive property.

$- 1 (4 x) - 1 (2 y) = (- 1) (6)$

$4 x - 5 y = - 1$

Multiply.

Multiply $4$ by $- 1$ .

$- 4 x - 1 (2 y) = (- 1) (6)$

$4 x - 5 y = - 1$

Multiply $2$ by $- 1$ .

$- 4 x - 2 y = (- 1) (6)$

$4 x - 5 y = - 1$

$- 4 x - 2 y = (- 1) (6)$

$4 x - 5 y = - 1$

$- 4 x - 2 y = (- 1) (6)$

$4 x - 5 y = - 1$

$- 4 x - 2 y = (- 1) (6)$

$4 x - 5 y = - 1$

Simplify the right side.

Multiply $- 1$ by $6$ .

$- 4 x - 2 y = - 6$

$4 x - 5 y = - 1$

$- 4 x - 2 y = - 6$

$4 x - 5 y = - 1$

$- 4 x - 2 y = - 6$

$4 x - 5 y = - 1$

Step 3

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

	$-$	$4$	$x$	$-$	$2$	$y$	$=$	$-$	$6$
$+$		$4$	$x$	$-$	$5$	$y$	$=$	$-$	$1$
				$-$	$7$	$y$	$=$	$-$	$7$

Step 4

Divide each term in $- 7 y = - 7$ by $- 7$ and simplify.

Divide each term in $- 7 y = - 7$ by $- 7$ .

$\frac{- 7 y}{- 7} = \frac{- 7}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 y}{- 7} = \frac{- 7}{- 7}$

Divide $y$ by $1$ .

$y = \frac{- 7}{- 7}$

Simplify the right side.

Divide $- 7$ by $- 7$ .

$y = 1$

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 $x$ .

$- 4 x - 2 \cdot 1 = - 6$

Multiply $- 2$ by $1$ .

$- 4 x - 2 = - 6$

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

Add $2$ to both sides of the equation.

$- 4 x = - 6 + 2$

Add $- 6$ and $2$ .

$- 4 x = - 4$

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

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

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

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 4$ by $- 4$ .

$x = 1$

Step 6

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

$(1, 1)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(1, 1)$

Equation Form:

$x = 1, y = 1$

Step 8

Solve by Addition/Elimination 4x+2y=6 4x-5y=-1

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