Solve by Substitution 2y=-7x+3 , -7x-6y=5

$2 y = - 7 x + 3$ , $- 7 x - 6 y = 5$

Step 1

Divide each term in $2 y = - 7 x + 3$ by $2$ and simplify.

Divide each term in $2 y = - 7 x + 3$ by $2$ .

$\frac{2 y}{2} = \frac{- 7 x}{2} + \frac{3}{2}$

$- 7 x - 6 y = 5$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{- 7 x}{2} + \frac{3}{2}$

$- 7 x - 6 y = 5$

Divide $y$ by $1$ .

$y = \frac{- 7 x}{2} + \frac{3}{2}$

$- 7 x - 6 y = 5$

$y = \frac{- 7 x}{2} + \frac{3}{2}$

$- 7 x - 6 y = 5$

$y = \frac{- 7 x}{2} + \frac{3}{2}$

$- 7 x - 6 y = 5$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{7 x}{2} + \frac{3}{2}$

$- 7 x - 6 y = 5$

$y = - \frac{7 x}{2} + \frac{3}{2}$

$- 7 x - 6 y = 5$

$y = - \frac{7 x}{2} + \frac{3}{2}$

$- 7 x - 6 y = 5$

Step 2

Replace all occurrences of $y$ with $- \frac{7 x}{2} + \frac{3}{2}$ in each equation.

Replace all occurrences of $y$ in $- 7 x - 6 y = 5$ with $- \frac{7 x}{2} + \frac{3}{2}$ .

$- 7 x - 6 (- \frac{7 x}{2} + \frac{3}{2}) = 5$

$y = - \frac{7 x}{2} + \frac{3}{2}$

Simplify the left side.

Simplify $- 7 x - 6 (- \frac{7 x}{2} + \frac{3}{2})$ .

Simplify each term.

Apply the distributive property.

$- 7 x - 6 (- \frac{7 x}{2}) - 6 (\frac{3}{2}) = 5$

$y = - \frac{7 x}{2} + \frac{3}{2}$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{7 x}{2}$ into the numerator.

$- 7 x - 6 \frac{- 7 x}{2} - 6 (\frac{3}{2}) = 5$

$y = - \frac{7 x}{2} + \frac{3}{2}$

Factor $2$ out of $- 6$ .

$- 7 x + 2 (- 3) (\frac{- 7 x}{2}) - 6 (\frac{3}{2}) = 5$

$y = - \frac{7 x}{2} + \frac{3}{2}$

Cancel the common factor.

$- 7 x + 2 \cdot (- 3 \frac{- 7 x}{2}) - 6 (\frac{3}{2}) = 5$

$y = - \frac{7 x}{2} + \frac{3}{2}$

Rewrite the expression.

$- 7 x - 3 (- 7 x) - 6 (\frac{3}{2}) = 5$

$y = - \frac{7 x}{2} + \frac{3}{2}$

$- 7 x - 3 (- 7 x) - 6 (\frac{3}{2}) = 5$

$y = - \frac{7 x}{2} + \frac{3}{2}$

Multiply $- 7$ by $- 3$ .

$- 7 x + 21 x - 6 (\frac{3}{2}) = 5$

$y = - \frac{7 x}{2} + \frac{3}{2}$

Cancel the common factor of $2$ .

Factor $2$ out of $- 6$ .

$- 7 x + 21 x + 2 (- 3) (\frac{3}{2}) = 5$

$y = - \frac{7 x}{2} + \frac{3}{2}$

Cancel the common factor.

$- 7 x + 21 x + 2 \cdot (- 3 (\frac{3}{2})) = 5$

$y = - \frac{7 x}{2} + \frac{3}{2}$

Rewrite the expression.

$- 7 x + 21 x - 3 \cdot 3 = 5$

$y = - \frac{7 x}{2} + \frac{3}{2}$

$- 7 x + 21 x - 3 \cdot 3 = 5$

$y = - \frac{7 x}{2} + \frac{3}{2}$

Multiply $- 3$ by $3$ .

$- 7 x + 21 x - 9 = 5$

$y = - \frac{7 x}{2} + \frac{3}{2}$

$- 7 x + 21 x - 9 = 5$

$y = - \frac{7 x}{2} + \frac{3}{2}$

Add $- 7 x$ and $21 x$ .

$14 x - 9 = 5$

$y = - \frac{7 x}{2} + \frac{3}{2}$

$14 x - 9 = 5$

$y = - \frac{7 x}{2} + \frac{3}{2}$

$14 x - 9 = 5$

$y = - \frac{7 x}{2} + \frac{3}{2}$

$14 x - 9 = 5$

$y = - \frac{7 x}{2} + \frac{3}{2}$

Step 3

Solve for $x$ in $14 x - 9 = 5$ .

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

Add $9$ to both sides of the equation.

$14 x = 5 + 9$

$y = - \frac{7 x}{2} + \frac{3}{2}$

Add $5$ and $9$ .

$14 x = 14$

$y = - \frac{7 x}{2} + \frac{3}{2}$

$14 x = 14$

$y = - \frac{7 x}{2} + \frac{3}{2}$

Divide each term in $14 x = 14$ by $14$ and simplify.

Divide each term in $14 x = 14$ by $14$ .

$\frac{14 x}{14} = \frac{14}{14}$

$y = - \frac{7 x}{2} + \frac{3}{2}$

Simplify the left side.

Cancel the common factor of $14$ .

Cancel the common factor.

$\frac{14 x}{14} = \frac{14}{14}$

$y = - \frac{7 x}{2} + \frac{3}{2}$

Divide $x$ by $1$ .

$x = \frac{14}{14}$

$y = - \frac{7 x}{2} + \frac{3}{2}$

$x = \frac{14}{14}$

$y = - \frac{7 x}{2} + \frac{3}{2}$

$x = \frac{14}{14}$

$y = - \frac{7 x}{2} + \frac{3}{2}$

Simplify the right side.

Divide $14$ by $14$ .

$x = 1$

$y = - \frac{7 x}{2} + \frac{3}{2}$

$x = 1$

$y = - \frac{7 x}{2} + \frac{3}{2}$

$x = 1$

$y = - \frac{7 x}{2} + \frac{3}{2}$

$x = 1$

$y = - \frac{7 x}{2} + \frac{3}{2}$

Step 4

Replace all occurrences of $x$ with $1$ in each equation.

Replace all occurrences of $x$ in $y = - \frac{7 x}{2} + \frac{3}{2}$ with $1$ .

$y = - \frac{7 (1)}{2} + \frac{3}{2}$

$x = 1$

Simplify the right side.

Simplify $- \frac{7 (1)}{2} + \frac{3}{2}$ .

Combine the numerators over the common denominator.

$y = \frac{- 7 \cdot 1 + 3}{2}$

$x = 1$

Simplify the expression.

Multiply $- 7$ by $1$ .

$y = \frac{- 7 + 3}{2}$

$x = 1$

Add $- 7$ and $3$ .

$y = \frac{- 4}{2}$

$x = 1$

Divide $- 4$ by $2$ .

$y = - 2$

$x = 1$

$y = - 2$

$x = 1$

$y = - 2$

$x = 1$

$y = - 2$

$x = 1$

$y = - 2$

$x = 1$

Step 5

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

$(1, - 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(1, - 2)$

Equation Form:

$x = 1, y = - 2$

Step 7

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