Solve by Substitution 4x+2y=10 , x-y=13

$4 x + 2 y = 10$ , $x - y = 13$

Step 1

Add $y$ to both sides of the equation.

$x = 13 + y$

$4 x + 2 y = 10$

Step 2

Replace all occurrences of $x$ with $13 + y$ in each equation.

Replace all occurrences of $x$ in $4 x + 2 y = 10$ with $13 + y$ .

$4 (13 + y) + 2 y = 10$

$x = 13 + y$

Simplify the left side.

Simplify $4 (13 + y) + 2 y$ .

Simplify each term.

Apply the distributive property.

$4 \cdot 13 + 4 y + 2 y = 10$

$x = 13 + y$

Multiply $4$ by $13$ .

$52 + 4 y + 2 y = 10$

$x = 13 + y$

$52 + 4 y + 2 y = 10$

$x = 13 + y$

Add $4 y$ and $2 y$ .

$52 + 6 y = 10$

$x = 13 + y$

$52 + 6 y = 10$

$x = 13 + y$

$52 + 6 y = 10$

$x = 13 + y$

$52 + 6 y = 10$

$x = 13 + y$

Step 3

Solve for $y$ in $52 + 6 y = 10$ .

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

Subtract $52$ from both sides of the equation.

$6 y = 10 - 52$

$x = 13 + y$

Subtract $52$ from $10$ .

$6 y = - 42$

$x = 13 + y$

$6 y = - 42$

$x = 13 + y$

Divide each term in $6 y = - 42$ by $6$ and simplify.

Divide each term in $6 y = - 42$ by $6$ .

$\frac{6 y}{6} = \frac{- 42}{6}$

$x = 13 + y$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 y}{6} = \frac{- 42}{6}$

$x = 13 + y$

Divide $y$ by $1$ .

$y = \frac{- 42}{6}$

$x = 13 + y$

$y = \frac{- 42}{6}$

$x = 13 + y$

$y = \frac{- 42}{6}$

$x = 13 + y$

Simplify the right side.

Divide $- 42$ by $6$ .

$y = - 7$

$x = 13 + y$

$y = - 7$

$x = 13 + y$

$y = - 7$

$x = 13 + y$

$y = - 7$

$x = 13 + y$

Step 4

Replace all occurrences of $y$ with $- 7$ in each equation.

Replace all occurrences of $y$ in $x = 13 + y$ with $- 7$ .

$x = 13 - 7$

$y = - 7$

Simplify $x = 13 - 7$ .

Simplify the left side.

Remove parentheses.

$x = 13 - 7$

$y = - 7$

$x = 13 - 7$

$y = - 7$

Simplify the right side.

Subtract $7$ from $13$ .

$x = 6$

$y = - 7$

$x = 6$

$y = - 7$

$x = 6$

$y = - 7$

$x = 6$

$y = - 7$

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(6, - 7)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(6, - 7)$

Equation Form:

$x = 6, y = - 7$

Step 7

Solve by Substitution 4x+2y=10 , x-y=13

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