Solve the System of Equations -3x+y=7 and -5x-4y=23

$- 3 x + y = 7$ and $- 5 x - 4 y = 23$

Step 1

Add $3 x$ to both sides of the equation.

$y = 7 + 3 x$

$- 5 x - 4 y = 23$

Step 2

Replace all occurrences of $y$ with $7 + 3 x$ in each equation.

Replace all occurrences of $y$ in $- 5 x - 4 y = 23$ with $7 + 3 x$ .

$- 5 x - 4 (7 + 3 x) = 23$

$y = 7 + 3 x$

Simplify the left side.

Simplify $- 5 x - 4 (7 + 3 x)$ .

Simplify each term.

Apply the distributive property.

$- 5 x - 4 \cdot 7 - 4 (3 x) = 23$

$y = 7 + 3 x$

Multiply $- 4$ by $7$ .

$- 5 x - 28 - 4 (3 x) = 23$

$y = 7 + 3 x$

Multiply $3$ by $- 4$ .

$- 5 x - 28 - 12 x = 23$

$y = 7 + 3 x$

$- 5 x - 28 - 12 x = 23$

$y = 7 + 3 x$

Subtract $12 x$ from $- 5 x$ .

$- 17 x - 28 = 23$

$y = 7 + 3 x$

$- 17 x - 28 = 23$

$y = 7 + 3 x$

$- 17 x - 28 = 23$

$y = 7 + 3 x$

$- 17 x - 28 = 23$

$y = 7 + 3 x$

Step 3

Solve for $x$ in $- 17 x - 28 = 23$ .

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

Add $28$ to both sides of the equation.

$- 17 x = 23 + 28$

$y = 7 + 3 x$

Add $23$ and $28$ .

$- 17 x = 51$

$y = 7 + 3 x$

$- 17 x = 51$

$y = 7 + 3 x$

Divide each term in $- 17 x = 51$ by $- 17$ and simplify.

Divide each term in $- 17 x = 51$ by $- 17$ .

$\frac{- 17 x}{- 17} = \frac{51}{- 17}$

$y = 7 + 3 x$

Simplify the left side.

Cancel the common factor of $- 17$ .

Cancel the common factor.

$\frac{- 17 x}{- 17} = \frac{51}{- 17}$

$y = 7 + 3 x$

Divide $x$ by $1$ .

$x = \frac{51}{- 17}$

$y = 7 + 3 x$

$x = \frac{51}{- 17}$

$y = 7 + 3 x$

$x = \frac{51}{- 17}$

$y = 7 + 3 x$

Simplify the right side.

Divide $51$ by $- 17$ .

$x = - 3$

$y = 7 + 3 x$

$x = - 3$

$y = 7 + 3 x$

$x = - 3$

$y = 7 + 3 x$

$x = - 3$

$y = 7 + 3 x$

Step 4

Replace all occurrences of $x$ with $- 3$ in each equation.

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

$y = 7 + 3 (- 3)$

$x = - 3$

Simplify the right side.

Simplify $7 + 3 (- 3)$ .

Multiply $3$ by $- 3$ .

$y = 7 - 9$

$x = - 3$

Subtract $9$ from $7$ .

$y = - 2$

$x = - 3$

$y = - 2$

$x = - 3$

$y = - 2$

$x = - 3$

$y = - 2$

$x = - 3$

Step 5

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

$(- 3, - 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 3, - 2)$

Equation Form:

$x = - 3, y = - 2$

Step 7

Solve the System of Equations -3x+y=7 and -5x-4y=23

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