Solve by Substitution x+2y=7 , 3x-2y=-3

$x + 2 y = 7$ , $3 x - 2 y = - 3$

Step 1

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

$x = 7 - 2 y$

$3 x - 2 y = - 3$

Step 2

Replace all occurrences of $x$ with $7 - 2 y$ in each equation.

Replace all occurrences of $x$ in $3 x - 2 y = - 3$ with $7 - 2 y$ .

$3 (7 - 2 y) - 2 y = - 3$

$x = 7 - 2 y$

Simplify the left side.

Simplify $3 (7 - 2 y) - 2 y$ .

Simplify each term.

Apply the distributive property.

$3 \cdot 7 + 3 (- 2 y) - 2 y = - 3$

$x = 7 - 2 y$

Multiply $3$ by $7$ .

$21 + 3 (- 2 y) - 2 y = - 3$

$x = 7 - 2 y$

Multiply $- 2$ by $3$ .

$21 - 6 y - 2 y = - 3$

$x = 7 - 2 y$

$21 - 6 y - 2 y = - 3$

$x = 7 - 2 y$

Subtract $2 y$ from $- 6 y$ .

$21 - 8 y = - 3$

$x = 7 - 2 y$

$21 - 8 y = - 3$

$x = 7 - 2 y$

$21 - 8 y = - 3$

$x = 7 - 2 y$

$21 - 8 y = - 3$

$x = 7 - 2 y$

Step 3

Solve for $y$ in $21 - 8 y = - 3$ .

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

Subtract $21$ from both sides of the equation.

$- 8 y = - 3 - 21$

$x = 7 - 2 y$

Subtract $21$ from $- 3$ .

$- 8 y = - 24$

$x = 7 - 2 y$

$- 8 y = - 24$

$x = 7 - 2 y$

Divide each term in $- 8 y = - 24$ by $- 8$ and simplify.

Divide each term in $- 8 y = - 24$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{- 24}{- 8}$

$x = 7 - 2 y$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{- 24}{- 8}$

$x = 7 - 2 y$

Divide $y$ by $1$ .

$y = \frac{- 24}{- 8}$

$x = 7 - 2 y$

$y = \frac{- 24}{- 8}$

$x = 7 - 2 y$

$y = \frac{- 24}{- 8}$

$x = 7 - 2 y$

Simplify the right side.

Divide $- 24$ by $- 8$ .

$y = 3$

$x = 7 - 2 y$

$y = 3$

$x = 7 - 2 y$

$y = 3$

$x = 7 - 2 y$

$y = 3$

$x = 7 - 2 y$

Step 4

Replace all occurrences of $y$ with $3$ in each equation.

Replace all occurrences of $y$ in $x = 7 - 2 y$ with $3$ .

$x = 7 - 2 \cdot 3$

$y = 3$

Simplify the right side.

Simplify $7 - 2 \cdot 3$ .

Multiply $- 2$ by $3$ .

$x = 7 - 6$

$y = 3$

Subtract $6$ from $7$ .

$x = 1$

$y = 3$

$x = 1$

$y = 3$

$x = 1$

$y = 3$

$x = 1$

$y = 3$

Step 5

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

$(1, 3)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(1, 3)$

Equation Form:

$x = 1, y = 3$

Step 7

Solve by Substitution x+2y=7 , 3x-2y=-3

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