Solve the System of Equations 4x+2y=8 4x+3y=16

$4 x + 2 y = 8$ $4 x + 3 y = 16$

Step 1

Solve for $x$ in $4 x + 2 y = 8$ .

Subtract $2 y$ from both sides of the equation.

$4 x = 8 - 2 y$

$4 x + 3 y = 16$

Divide each term in $4 x = 8 - 2 y$ by $4$ and simplify.

Divide each term in $4 x = 8 - 2 y$ by $4$ .

$\frac{4 x}{4} = \frac{8}{4} + \frac{- 2 y}{4}$

$4 x + 3 y = 16$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{8}{4} + \frac{- 2 y}{4}$

$4 x + 3 y = 16$

Divide $x$ by $1$ .

$x = \frac{8}{4} + \frac{- 2 y}{4}$

$4 x + 3 y = 16$

$x = \frac{8}{4} + \frac{- 2 y}{4}$

$4 x + 3 y = 16$

$x = \frac{8}{4} + \frac{- 2 y}{4}$

$4 x + 3 y = 16$

Simplify the right side.

Simplify each term.

Divide $8$ by $4$ .

$x = 2 + \frac{- 2 y}{4}$

$4 x + 3 y = 16$

Cancel the common factor of $- 2$ and $4$ .

Factor $2$ out of $- 2 y$ .

$x = 2 + \frac{2 (- y)}{4}$

$4 x + 3 y = 16$

Cancel the common factors.

Factor $2$ out of $4$ .

$x = 2 + \frac{2 (- y)}{2 (2)}$

$4 x + 3 y = 16$

Cancel the common factor.

$x = 2 + \frac{2 (- y)}{2 \cdot 2}$

$4 x + 3 y = 16$

Rewrite the expression.

$x = 2 + \frac{- y}{2}$

$4 x + 3 y = 16$

$x = 2 + \frac{- y}{2}$

$4 x + 3 y = 16$

$x = 2 + \frac{- y}{2}$

$4 x + 3 y = 16$

Move the negative in front of the fraction.

$x = 2 - \frac{y}{2}$

$4 x + 3 y = 16$

$x = 2 - \frac{y}{2}$

$4 x + 3 y = 16$

$x = 2 - \frac{y}{2}$

$4 x + 3 y = 16$

$x = 2 - \frac{y}{2}$

$4 x + 3 y = 16$

$x = 2 - \frac{y}{2}$

$4 x + 3 y = 16$

Step 2

Replace all occurrences of $x$ with $2 - \frac{y}{2}$ in each equation.

Replace all occurrences of $x$ in $4 x + 3 y = 16$ with $2 - \frac{y}{2}$ .

$4 (2 - \frac{y}{2}) + 3 y = 16$

$x = 2 - \frac{y}{2}$

Simplify the left side.

Simplify $4 (2 - \frac{y}{2}) + 3 y$ .

Simplify each term.

Apply the distributive property.

$4 \cdot 2 + 4 (- \frac{y}{2}) + 3 y = 16$

$x = 2 - \frac{y}{2}$

Multiply $4$ by $2$ .

$8 + 4 (- \frac{y}{2}) + 3 y = 16$

$x = 2 - \frac{y}{2}$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{y}{2}$ into the numerator.

$8 + 4 (\frac{- y}{2}) + 3 y = 16$

$x = 2 - \frac{y}{2}$

Factor $2$ out of $4$ .

$8 + 2 (2) (\frac{- y}{2}) + 3 y = 16$

$x = 2 - \frac{y}{2}$

Cancel the common factor.

$8 + 2 \cdot (2 (\frac{- y}{2})) + 3 y = 16$

$x = 2 - \frac{y}{2}$

Rewrite the expression.

$8 + 2 (- y) + 3 y = 16$

$x = 2 - \frac{y}{2}$

$8 + 2 (- y) + 3 y = 16$

$x = 2 - \frac{y}{2}$

Multiply $- 1$ by $2$ .

$8 - 2 y + 3 y = 16$

$x = 2 - \frac{y}{2}$

$8 - 2 y + 3 y = 16$

$x = 2 - \frac{y}{2}$

Add $- 2 y$ and $3 y$ .

$8 + y = 16$

$x = 2 - \frac{y}{2}$

$8 + y = 16$

$x = 2 - \frac{y}{2}$

$8 + y = 16$

$x = 2 - \frac{y}{2}$

$8 + y = 16$

$x = 2 - \frac{y}{2}$

Step 3

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

Subtract $8$ from both sides of the equation.

$y = 16 - 8$

$x = 2 - \frac{y}{2}$

Subtract $8$ from $16$ .

$y = 8$

$x = 2 - \frac{y}{2}$

$y = 8$

$x = 2 - \frac{y}{2}$

Step 4

Replace all occurrences of $y$ with $8$ in each equation.

Replace all occurrences of $y$ in $x = 2 - \frac{y}{2}$ with $8$ .

$x = 2 - \frac{8}{2}$

$y = 8$

Simplify the right side.

Simplify $2 - \frac{8}{2}$ .

Simplify each term.

Divide $8$ by $2$ .

$x = 2 - 1 \cdot 4$

$y = 8$

Multiply $- 1$ by $4$ .

$x = 2 - 4$

$y = 8$

$x = 2 - 4$

$y = 8$

Subtract $4$ from $2$ .

$x = - 2$

$y = 8$

$x = - 2$

$y = 8$

$x = - 2$

$y = 8$

$x = - 2$

$y = 8$

Step 5

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

$(- 2, 8)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 2, 8)$

Equation Form:

$x = - 2, y = 8$

Step 7

Solve the System of Equations 4x+2y=8 4x+3y=16

Related Questions

Support LCMGCF.com by disabling your adblocker.