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

$5 x + y = 6$ , $2 y = x + 1$

Step 1

Move all terms containing variables to the left side of the equation.

Subtract $x$ from both sides of the equation.

$2 y - x = 1$

$5 x + y = 6$

Reorder $2 y$ and $- x$ .

$- x + 2 y = 1$

$5 x + y = 6$

$- x + 2 y = 1$

$5 x + y = 6$

Step 2

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

$(- 2) \cdot (5 x + y) = (- 2) (6)$

$- x + 2 y = 1$

Step 3

Simplify.

Simplify the left side.

Simplify $(- 2) \cdot (5 x + y)$ .

Apply the distributive property.

$- 2 (5 x) - 2 y = (- 2) (6)$

$- x + 2 y = 1$

Multiply $5$ by $- 2$ .

$- 10 x - 2 y = (- 2) (6)$

$- x + 2 y = 1$

$- 10 x - 2 y = (- 2) (6)$

$- x + 2 y = 1$

$- 10 x - 2 y = (- 2) (6)$

$- x + 2 y = 1$

Simplify the right side.

Multiply $- 2$ by $6$ .

$- 10 x - 2 y = - 12$

$- x + 2 y = 1$

$- 10 x - 2 y = - 12$

$- x + 2 y = 1$

$- 10 x - 2 y = - 12$

$- x + 2 y = 1$

Step 4

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

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

Step 5

Divide each term in $- 11 x = - 11$ by $- 11$ and simplify.

Divide each term in $- 11 x = - 11$ by $- 11$ .

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

Simplify the left side.

Cancel the common factor of $- 11$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 11$ by $- 11$ .

$x = 1$

Step 6

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

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

$- 10 \cdot 1 - 2 y = - 12$

Multiply $- 10$ by $1$ .

$- 10 - 2 y = - 12$

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

Add $10$ to both sides of the equation.

$- 2 y = - 12 + 10$

Add $- 12$ and $10$ .

$- 2 y = - 2$

Divide each term in $- 2 y = - 2$ by $- 2$ and simplify.

Divide each term in $- 2 y = - 2$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{- 2}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{- 2}{- 2}$

Divide $y$ by $1$ .

$y = \frac{- 2}{- 2}$

Simplify the right side.

Divide $- 2$ by $- 2$ .

$y = 1$

Step 7

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

$(1, 1)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(1, 1)$

Equation Form:

$x = 1, y = 1$

Step 9

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

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