Solve by Substitution -7x+y=-19 , -2x+3y=-19

$- 7 x + y = - 19$ , $- 2 x + 3 y = - 19$

Step 1

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

$y = - 19 + 7 x$

$- 2 x + 3 y = - 19$

Step 2

Replace all occurrences of $y$ with $- 19 + 7 x$ in each equation.

Replace all occurrences of $y$ in $- 2 x + 3 y = - 19$ with $- 19 + 7 x$ .

$- 2 x + 3 (- 19 + 7 x) = - 19$

$y = - 19 + 7 x$

Simplify the left side.

Simplify $- 2 x + 3 (- 19 + 7 x)$ .

Simplify each term.

Apply the distributive property.

$- 2 x + 3 \cdot - 19 + 3 (7 x) = - 19$

$y = - 19 + 7 x$

Multiply $3$ by $- 19$ .

$- 2 x - 57 + 3 (7 x) = - 19$

$y = - 19 + 7 x$

Multiply $7$ by $3$ .

$- 2 x - 57 + 21 x = - 19$

$y = - 19 + 7 x$

$- 2 x - 57 + 21 x = - 19$

$y = - 19 + 7 x$

Add $- 2 x$ and $21 x$ .

$19 x - 57 = - 19$

$y = - 19 + 7 x$

$19 x - 57 = - 19$

$y = - 19 + 7 x$

$19 x - 57 = - 19$

$y = - 19 + 7 x$

$19 x - 57 = - 19$

$y = - 19 + 7 x$

Step 3

Solve for $x$ in $19 x - 57 = - 19$ .

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

Add $57$ to both sides of the equation.

$19 x = - 19 + 57$

$y = - 19 + 7 x$

Add $- 19$ and $57$ .

$19 x = 38$

$y = - 19 + 7 x$

$19 x = 38$

$y = - 19 + 7 x$

Divide each term in $19 x = 38$ by $19$ and simplify.

Divide each term in $19 x = 38$ by $19$ .

$\frac{19 x}{19} = \frac{38}{19}$

$y = - 19 + 7 x$

Simplify the left side.

Cancel the common factor of $19$ .

Cancel the common factor.

$\frac{19 x}{19} = \frac{38}{19}$

$y = - 19 + 7 x$

Divide $x$ by $1$ .

$x = \frac{38}{19}$

$y = - 19 + 7 x$

$x = \frac{38}{19}$

$y = - 19 + 7 x$

$x = \frac{38}{19}$

$y = - 19 + 7 x$

Simplify the right side.

Divide $38$ by $19$ .

$x = 2$

$y = - 19 + 7 x$

$x = 2$

$y = - 19 + 7 x$

$x = 2$

$y = - 19 + 7 x$

$x = 2$

$y = - 19 + 7 x$

Step 4

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

Replace all occurrences of $x$ in $y = - 19 + 7 x$ with $2$ .

$y = - 19 + 7 (2)$

$x = 2$

Simplify the right side.

Simplify $- 19 + 7 (2)$ .

Multiply $7$ by $2$ .

$y = - 19 + 14$

$x = 2$

Add $- 19$ and $14$ .

$y = - 5$

$x = 2$

$y = - 5$

$x = 2$

$y = - 5$

$x = 2$

$y = - 5$

$x = 2$

Step 5

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

$(2, - 5)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(2, - 5)$

Equation Form:

$x = 2, y = - 5$

Step 7

Solve by Substitution -7x+y=-19 , -2x+3y=-19

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