Solve by Substitution -7x+y=-30 2x-5=y

$- 7 x + y = - 30$ $2 x - 5 = y$

Step 1

Add $7 x$ to both sides of the equation.

$y = - 30 + 7 x$

$2 x - 5 = y$

Step 2

Replace all occurrences of $y$ with $- 30 + 7 x$ in each equation.

Replace all occurrences of $y$ in $2 x - 5 = y$ with $- 30 + 7 x$ .

$2 x - 5 = - 30 + 7 x$

$y = - 30 + 7 x$

Simplify the left side.

Remove parentheses.

$2 x - 5 = - 30 + 7 x$

$y = - 30 + 7 x$

$2 x - 5 = - 30 + 7 x$

$y = - 30 + 7 x$

$2 x - 5 = - 30 + 7 x$

$y = - 30 + 7 x$

Step 3

Solve for $x$ in $2 x - 5 = - 30 + 7 x$ .

Move all terms containing $x$ to the left side of the equation.

Subtract $7 x$ from both sides of the equation.

$2 x - 5 - 7 x = - 30$

$y = - 30 + 7 x$

Subtract $7 x$ from $2 x$ .

$- 5 x - 5 = - 30$

$y = - 30 + 7 x$

$- 5 x - 5 = - 30$

$y = - 30 + 7 x$

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

Add $5$ to both sides of the equation.

$- 5 x = - 30 + 5$

$y = - 30 + 7 x$

Add $- 30$ and $5$ .

$- 5 x = - 25$

$y = - 30 + 7 x$

$- 5 x = - 25$

$y = - 30 + 7 x$

Divide each term in $- 5 x = - 25$ by $- 5$ and simplify.

Divide each term in $- 5 x = - 25$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{- 25}{- 5}$

$y = - 30 + 7 x$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{- 25}{- 5}$

$y = - 30 + 7 x$

Divide $x$ by $1$ .

$x = \frac{- 25}{- 5}$

$y = - 30 + 7 x$

$x = \frac{- 25}{- 5}$

$y = - 30 + 7 x$

$x = \frac{- 25}{- 5}$

$y = - 30 + 7 x$

Simplify the right side.

Divide $- 25$ by $- 5$ .

$x = 5$

$y = - 30 + 7 x$

$x = 5$

$y = - 30 + 7 x$

$x = 5$

$y = - 30 + 7 x$

$x = 5$

$y = - 30 + 7 x$

Step 4

Replace all occurrences of $x$ with $5$ in each equation.

Replace all occurrences of $x$ in $y = - 30 + 7 x$ with $5$ .

$y = - 30 + 7 (5)$

$x = 5$

Simplify the right side.

Simplify $- 30 + 7 (5)$ .

Multiply $7$ by $5$ .

$y = - 30 + 35$

$x = 5$

Add $- 30$ and $35$ .

$y = 5$

$x = 5$

$y = 5$

$x = 5$

$y = 5$

$x = 5$

$y = 5$

$x = 5$

Step 5

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

$(5, 5)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(5, 5)$

Equation Form:

$x = 5, y = 5$

Step 7

Solve by Substitution -7x+y=-30 2x-5=y

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