Solve by Substitution -5x+3y=12 , x+2y=8

$- 5 x + 3 y = 12$ , $x + 2 y = 8$

Step 1

Subtract $2 y$ from both sides of the equation.

$x = 8 - 2 y$

$- 5 x + 3 y = 12$

Step 2

Replace all occurrences of $x$ with $8 - 2 y$ in each equation.

Replace all occurrences of $x$ in $- 5 x + 3 y = 12$ with $8 - 2 y$ .

$- 5 (8 - 2 y) + 3 y = 12$

$x = 8 - 2 y$

Simplify the left side.

Simplify $- 5 (8 - 2 y) + 3 y$ .

Simplify each term.

Apply the distributive property.

$- 5 \cdot 8 - 5 (- 2 y) + 3 y = 12$

$x = 8 - 2 y$

Multiply $- 5$ by $8$ .

$- 40 - 5 (- 2 y) + 3 y = 12$

$x = 8 - 2 y$

Multiply $- 2$ by $- 5$ .

$- 40 + 10 y + 3 y = 12$

$x = 8 - 2 y$

$- 40 + 10 y + 3 y = 12$

$x = 8 - 2 y$

Add $10 y$ and $3 y$ .

$- 40 + 13 y = 12$

$x = 8 - 2 y$

$- 40 + 13 y = 12$

$x = 8 - 2 y$

$- 40 + 13 y = 12$

$x = 8 - 2 y$

$- 40 + 13 y = 12$

$x = 8 - 2 y$

Step 3

Solve for $y$ in $- 40 + 13 y = 12$ .

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

Add $40$ to both sides of the equation.

$13 y = 12 + 40$

$x = 8 - 2 y$

Add $12$ and $40$ .

$13 y = 52$

$x = 8 - 2 y$

$13 y = 52$

$x = 8 - 2 y$

Divide each term in $13 y = 52$ by $13$ and simplify.

Divide each term in $13 y = 52$ by $13$ .

$\frac{13 y}{13} = \frac{52}{13}$

$x = 8 - 2 y$

Simplify the left side.

Cancel the common factor of $13$ .

Cancel the common factor.

$\frac{13 y}{13} = \frac{52}{13}$

$x = 8 - 2 y$

Divide $y$ by $1$ .

$y = \frac{52}{13}$

$x = 8 - 2 y$

$y = \frac{52}{13}$

$x = 8 - 2 y$

$y = \frac{52}{13}$

$x = 8 - 2 y$

Simplify the right side.

Divide $52$ by $13$ .

$y = 4$

$x = 8 - 2 y$

$y = 4$

$x = 8 - 2 y$

$y = 4$

$x = 8 - 2 y$

$y = 4$

$x = 8 - 2 y$

Step 4

Replace all occurrences of $y$ with $4$ in each equation.

Replace all occurrences of $y$ in $x = 8 - 2 y$ with $4$ .

$x = 8 - 2 \cdot 4$

$y = 4$

Simplify the right side.

Simplify $8 - 2 \cdot 4$ .

Multiply $- 2$ by $4$ .

$x = 8 - 8$

$y = 4$

Subtract $8$ from $8$ .

$x = 0$

$y = 4$

$x = 0$

$y = 4$

$x = 0$

$y = 4$

$x = 0$

$y = 4$

Step 5

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

$(0, 4)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(0, 4)$

Equation Form:

$x = 0, y = 4$

Step 7

Solve by Substitution -5x+3y=12 , x+2y=8

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