Solve the System of Equations 4x+10y=-24 -2x+y=-24

$4 x + 10 y = - 24$ $- 2 x + y = - 24$

Step 1

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

$y = - 24 + 2 x$

$4 x + 10 y = - 24$

Step 2

Replace all occurrences of $y$ with $- 24 + 2 x$ in each equation.

Replace all occurrences of $y$ in $4 x + 10 y = - 24$ with $- 24 + 2 x$ .

$4 x + 10 (- 24 + 2 x) = - 24$

$y = - 24 + 2 x$

Simplify the left side.

Simplify $4 x + 10 (- 24 + 2 x)$ .

Simplify each term.

Apply the distributive property.

$4 x + 10 \cdot - 24 + 10 (2 x) = - 24$

$y = - 24 + 2 x$

Multiply $10$ by $- 24$ .

$4 x - 240 + 10 (2 x) = - 24$

$y = - 24 + 2 x$

Multiply $2$ by $10$ .

$4 x - 240 + 20 x = - 24$

$y = - 24 + 2 x$

$4 x - 240 + 20 x = - 24$

$y = - 24 + 2 x$

Add $4 x$ and $20 x$ .

$24 x - 240 = - 24$

$y = - 24 + 2 x$

$24 x - 240 = - 24$

$y = - 24 + 2 x$

$24 x - 240 = - 24$

$y = - 24 + 2 x$

$24 x - 240 = - 24$

$y = - 24 + 2 x$

Step 3

Solve for $x$ in $24 x - 240 = - 24$ .

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

Add $240$ to both sides of the equation.

$24 x = - 24 + 240$

$y = - 24 + 2 x$

Add $- 24$ and $240$ .

$24 x = 216$

$y = - 24 + 2 x$

$24 x = 216$

$y = - 24 + 2 x$

Divide each term in $24 x = 216$ by $24$ and simplify.

Divide each term in $24 x = 216$ by $24$ .

$\frac{24 x}{24} = \frac{216}{24}$

$y = - 24 + 2 x$

Simplify the left side.

Cancel the common factor of $24$ .

Cancel the common factor.

$\frac{24 x}{24} = \frac{216}{24}$

$y = - 24 + 2 x$

Divide $x$ by $1$ .

$x = \frac{216}{24}$

$y = - 24 + 2 x$

$x = \frac{216}{24}$

$y = - 24 + 2 x$

$x = \frac{216}{24}$

$y = - 24 + 2 x$

Simplify the right side.

Divide $216$ by $24$ .

$x = 9$

$y = - 24 + 2 x$

$x = 9$

$y = - 24 + 2 x$

$x = 9$

$y = - 24 + 2 x$

$x = 9$

$y = - 24 + 2 x$

Step 4

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

Replace all occurrences of $x$ in $y = - 24 + 2 x$ with $9$ .

$y = - 24 + 2 (9)$

$x = 9$

Simplify the right side.

Simplify $- 24 + 2 (9)$ .

Multiply $2$ by $9$ .

$y = - 24 + 18$

$x = 9$

Add $- 24$ and $18$ .

$y = - 6$

$x = 9$

$y = - 6$

$x = 9$

$y = - 6$

$x = 9$

$y = - 6$

$x = 9$

Step 5

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

$(9, - 6)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(9, - 6)$

Equation Form:

$x = 9, y = - 6$

Step 7

Solve the System of Equations 4x+10y=-24 -2x+y=-24

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