Solve the System of Equations x-2y=-19 and -3x+5y=48

$x - 2 y = - 19$ and $- 3 x + 5 y = 48$

Add $2 y$ to both sides of the equation.

$x = - 19 + 2 y$

$- 3 x + 5 y = 48$

Replace all occurrences of $x$ with $- 19 + 2 y$ in each equation.

Replace all occurrences of $x$ in $- 3 x + 5 y = 48$ with $- 19 + 2 y$ .

$- 3 (- 19 + 2 y) + 5 y = 48$

$x = - 19 + 2 y$

Simplify the left side.

Simplify $- 3 (- 19 + 2 y) + 5 y$ .

Simplify each term.

Apply the distributive property.

$- 3 \cdot - 19 - 3 (2 y) + 5 y = 48$

$x = - 19 + 2 y$

Multiply $- 3$ by $- 19$ .

$57 - 3 (2 y) + 5 y = 48$

$x = - 19 + 2 y$

Multiply $2$ by $- 3$ .

$57 - 6 y + 5 y = 48$

$x = - 19 + 2 y$

$57 - 6 y + 5 y = 48$

$x = - 19 + 2 y$

Add $- 6 y$ and $5 y$ .

$57 - y = 48$

$x = - 19 + 2 y$

$57 - y = 48$

$x = - 19 + 2 y$

$57 - y = 48$

$x = - 19 + 2 y$

$57 - y = 48$

$x = - 19 + 2 y$

Solve for $y$ in $57 - y = 48$ .

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

Subtract $57$ from both sides of the equation.

$- y = 48 - 57$

$x = - 19 + 2 y$

Subtract $57$ from $48$ .

$- y = - 9$

$x = - 19 + 2 y$

$- y = - 9$

$x = - 19 + 2 y$

Divide each term in $- y = - 9$ by $- 1$ and simplify.

Divide each term in $- y = - 9$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 9}{- 1}$

$x = - 19 + 2 y$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 9}{- 1}$

$x = - 19 + 2 y$

Divide $y$ by $1$ .

$y = \frac{- 9}{- 1}$

$x = - 19 + 2 y$

$y = \frac{- 9}{- 1}$

$x = - 19 + 2 y$

Simplify the right side.

Divide $- 9$ by $- 1$ .

$y = 9$

$x = - 19 + 2 y$

$y = 9$

$x = - 19 + 2 y$

$y = 9$

$x = - 19 + 2 y$

$y = 9$

$x = - 19 + 2 y$

Replace all occurrences of $y$ with $9$ in each equation.

Replace all occurrences of $y$ in $x = - 19 + 2 y$ with $9$ .

$x = - 19 + 2 (9)$

$y = 9$

Simplify the right side.

Simplify $- 19 + 2 (9)$ .

Multiply $2$ by $9$ .

$x = - 19 + 18$

$y = 9$

Add $- 19$ and $18$ .

$x = - 1$

$y = 9$

$x = - 1$

$y = 9$

$x = - 1$

$y = 9$

$x = - 1$

$y = 9$

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

$(- 1, 9)$

The result can be shown in multiple forms.

Point Form:

$(- 1, 9)$

Equation Form:

$x = - 1, y = 9$

Solve the System of Equations x-2y=-19 and -3x+5y=48

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