Solve by Substitution 2x-y=-7 , 4x-y=-4

$2 x - y = - 7$ , $4 x - y = - 4$

Step 1

Solve for $x$ in $2 x - y = - 7$ .

Add $y$ to both sides of the equation.

$2 x = - 7 + y$

$4 x - y = - 4$

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

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

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

$4 x - y = - 4$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

$4 x - y = - 4$

Divide $x$ by $1$ .

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

$4 x - y = - 4$

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

$4 x - y = - 4$

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

$4 x - y = - 4$

Simplify the right side.

Move the negative in front of the fraction.

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

$4 x - y = - 4$

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

$4 x - y = - 4$

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

$4 x - y = - 4$

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

$4 x - y = - 4$

Step 2

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

Replace all occurrences of $x$ in $4 x - y = - 4$ with $- \frac{7}{2} + \frac{y}{2}$ .

$4 (- \frac{7}{2} + \frac{y}{2}) - y = - 4$

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

Simplify the left side.

Simplify $4 (- \frac{7}{2} + \frac{y}{2}) - y$ .

Simplify each term.

Apply the distributive property.

$4 (- \frac{7}{2}) + 4 (\frac{y}{2}) - y = - 4$

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

Cancel the common factor of $2$ .

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

$4 (\frac{- 7}{2}) + 4 (\frac{y}{2}) - y = - 4$

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

Factor $2$ out of $4$ .

$2 (2) (\frac{- 7}{2}) + 4 (\frac{y}{2}) - y = - 4$

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

Cancel the common factor.

$2 \cdot (2 (\frac{- 7}{2})) + 4 (\frac{y}{2}) - y = - 4$

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

Rewrite the expression.

$2 \cdot - 7 + 4 (\frac{y}{2}) - y = - 4$

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

$2 \cdot - 7 + 4 (\frac{y}{2}) - y = - 4$

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

Multiply $2$ by $- 7$ .

$- 14 + 4 (\frac{y}{2}) - y = - 4$

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

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$- 14 + 2 (2) (\frac{y}{2}) - y = - 4$

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

Cancel the common factor.

$- 14 + 2 \cdot (2 (\frac{y}{2})) - y = - 4$

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

Rewrite the expression.

$- 14 + 2 y - y = - 4$

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

$- 14 + 2 y - y = - 4$

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

$- 14 + 2 y - y = - 4$

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

Subtract $y$ from $2 y$ .

$- 14 + y = - 4$

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

$- 14 + y = - 4$

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

$- 14 + y = - 4$

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

$- 14 + y = - 4$

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

Step 3

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

Add $14$ to both sides of the equation.

$y = - 4 + 14$

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

Add $- 4$ and $14$ .

$y = 10$

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

$y = 10$

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

Step 4

Replace all occurrences of $y$ with $10$ in each equation.

Replace all occurrences of $y$ in $x = - \frac{7}{2} + \frac{y}{2}$ with $10$ .

$x = - \frac{7}{2} + \frac{10}{2}$

$y = 10$

Simplify the right side.

Simplify $- \frac{7}{2} + \frac{10}{2}$ .

Combine the numerators over the common denominator.

$x = \frac{- 7 + 10}{2}$

$y = 10$

Add $- 7$ and $10$ .

$x = \frac{3}{2}$

$y = 10$

$x = \frac{3}{2}$

$y = 10$

$x = \frac{3}{2}$

$y = 10$

$x = \frac{3}{2}$

$y = 10$

Step 5

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

$(\frac{3}{2}, 10)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(\frac{3}{2}, 10)$

Equation Form:

$x = \frac{3}{2}, y = 10$

Step 7

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