Solve by Graphing 3x+7y=7 5x-7y=-63

$3 x + 7 y = 7$ $5 x - 7 y = - 63$

Step 1

Subtract $3 x$ from both sides of the equation.

$7 y = 7 - 3 x$

$5 x - 7 y = - 63$

Step 2

Divide each term in $7 y = 7 - 3 x$ by $7$ and simplify.

Divide each term in $7 y = 7 - 3 x$ by $7$ .

$\frac{7 y}{7} = \frac{7}{7} + \frac{- 3 x}{7}$

$5 x - 7 y = - 63$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 y}{7} = \frac{7}{7} + \frac{- 3 x}{7}$

$5 x - 7 y = - 63$

Divide $y$ by $1$ .

$y = \frac{7}{7} + \frac{- 3 x}{7}$

$5 x - 7 y = - 63$

$y = \frac{7}{7} + \frac{- 3 x}{7}$

$5 x - 7 y = - 63$

$y = \frac{7}{7} + \frac{- 3 x}{7}$

$5 x - 7 y = - 63$

Simplify the right side.

Simplify each term.

Divide $7$ by $7$ .

$y = 1 + \frac{- 3 x}{7}$

$5 x - 7 y = - 63$

Move the negative in front of the fraction.

$y = 1 - \frac{3 x}{7}$

$5 x - 7 y = - 63$

$y = 1 - \frac{3 x}{7}$

$5 x - 7 y = - 63$

$y = 1 - \frac{3 x}{7}$

$5 x - 7 y = - 63$

$y = 1 - \frac{3 x}{7}$

$5 x - 7 y = - 63$

Step 3

Subtract $5 x$ from both sides of the equation.

$- 7 y = - 63 - 5 x$

$y = 1 - \frac{3 x}{7}$

Step 4

Divide each term in $- 7 y = - 63 - 5 x$ by $- 7$ and simplify.

Divide each term in $- 7 y = - 63 - 5 x$ by $- 7$ .

$\frac{- 7 y}{- 7} = \frac{- 63}{- 7} + \frac{- 5 x}{- 7}$

$y = 1 - \frac{3 x}{7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 y}{- 7} = \frac{- 63}{- 7} + \frac{- 5 x}{- 7}$

$y = 1 - \frac{3 x}{7}$

Divide $y$ by $1$ .

$y = \frac{- 63}{- 7} + \frac{- 5 x}{- 7}$

$y = 1 - \frac{3 x}{7}$

$y = \frac{- 63}{- 7} + \frac{- 5 x}{- 7}$

$y = 1 - \frac{3 x}{7}$

$y = \frac{- 63}{- 7} + \frac{- 5 x}{- 7}$

$y = 1 - \frac{3 x}{7}$

Simplify the right side.

Simplify each term.

Divide $- 63$ by $- 7$ .

$y = 9 + \frac{- 5 x}{- 7}$

$y = 1 - \frac{3 x}{7}$

Dividing two negative values results in a positive value.

$y = 9 + \frac{5 x}{7}$

$y = 1 - \frac{3 x}{7}$

$y = 9 + \frac{5 x}{7}$

$y = 1 - \frac{3 x}{7}$

$y = 9 + \frac{5 x}{7}$

$y = 1 - \frac{3 x}{7}$

$y = 9 + \frac{5 x}{7}$

$y = 1 - \frac{3 x}{7}$

Step 5

Create a graph to locate the intersection of the equations. The intersection of the system of equations is the solution.

$(- 7, 4)$

Step 6

Solve by Graphing 3x+7y=7 5x-7y=-63

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