Solve the System of Equations 2x-3y=-2 and 4x+y=24

$2 x - 3 y = - 2$ and $4 x + y = 24$

Step 1

Subtract $4 x$ from both sides of the equation.

$y = 24 - 4 x$

$2 x - 3 y = - 2$

Step 2

Replace all occurrences of $y$ with $24 - 4 x$ in each equation.

Replace all occurrences of $y$ in $2 x - 3 y = - 2$ with $24 - 4 x$ .

$2 x - 3 (24 - 4 x) = - 2$

$y = 24 - 4 x$

Simplify the left side.

Simplify $2 x - 3 (24 - 4 x)$ .

Simplify each term.

Apply the distributive property.

$2 x - 3 \cdot 24 - 3 (- 4 x) = - 2$

$y = 24 - 4 x$

Multiply $- 3$ by $24$ .

$2 x - 72 - 3 (- 4 x) = - 2$

$y = 24 - 4 x$

Multiply $- 4$ by $- 3$ .

$2 x - 72 + 12 x = - 2$

$y = 24 - 4 x$

$2 x - 72 + 12 x = - 2$

$y = 24 - 4 x$

Add $2 x$ and $12 x$ .

$14 x - 72 = - 2$

$y = 24 - 4 x$

$14 x - 72 = - 2$

$y = 24 - 4 x$

$14 x - 72 = - 2$

$y = 24 - 4 x$

$14 x - 72 = - 2$

$y = 24 - 4 x$

Step 3

Solve for $x$ in $14 x - 72 = - 2$ .

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

Add $72$ to both sides of the equation.

$14 x = - 2 + 72$

$y = 24 - 4 x$

Add $- 2$ and $72$ .

$14 x = 70$

$y = 24 - 4 x$

$14 x = 70$

$y = 24 - 4 x$

Divide each term in $14 x = 70$ by $14$ and simplify.

Divide each term in $14 x = 70$ by $14$ .

$\frac{14 x}{14} = \frac{70}{14}$

$y = 24 - 4 x$

Simplify the left side.

Cancel the common factor of $14$ .

Cancel the common factor.

$\frac{14 x}{14} = \frac{70}{14}$

$y = 24 - 4 x$

Divide $x$ by $1$ .

$x = \frac{70}{14}$

$y = 24 - 4 x$

$x = \frac{70}{14}$

$y = 24 - 4 x$

$x = \frac{70}{14}$

$y = 24 - 4 x$

Simplify the right side.

Divide $70$ by $14$ .

$x = 5$

$y = 24 - 4 x$

$x = 5$

$y = 24 - 4 x$

$x = 5$

$y = 24 - 4 x$

$x = 5$

$y = 24 - 4 x$

Step 4

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

Replace all occurrences of $x$ in $y = 24 - 4 x$ with $5$ .

$y = 24 - 4 \cdot 5$

$x = 5$

Simplify the right side.

Simplify $24 - 4 \cdot 5$ .

Multiply $- 4$ by $5$ .

$y = 24 - 20$

$x = 5$

Subtract $20$ from $24$ .

$y = 4$

$x = 5$

$y = 4$

$x = 5$

$y = 4$

$x = 5$

$y = 4$

$x = 5$

Step 5

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

$(5, 4)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(5, 4)$

Equation Form:

$x = 5, y = 4$

Step 7

Solve the System of Equations 2x-3y=-2 and 4x+y=24

Related Questions

Support LCMGCF.com by disabling your adblocker.