Solve the System of Equations 3x+4y=36 y=-1/2x+8

$3 x + 4 y = 36$ $y = - \frac{1}{2} x + 8$

Step 1

Combine $x$ and $\frac{1}{2}$ .

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

$3 x + 4 y = 36$

Step 2

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

Replace all occurrences of $y$ in $3 x + 4 y = 36$ with $- \frac{x}{2} + 8$ .

$3 x + 4 (- \frac{x}{2} + 8) = 36$

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

Simplify the left side.

Simplify $3 x + 4 (- \frac{x}{2} + 8)$ .

Simplify each term.

Apply the distributive property.

$3 x + 4 (- \frac{x}{2}) + 4 \cdot 8 = 36$

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

Cancel the common factor of $2$ .

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

$3 x + 4 (\frac{- x}{2}) + 4 \cdot 8 = 36$

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

Factor $2$ out of $4$ .

$3 x + 2 (2) (\frac{- x}{2}) + 4 \cdot 8 = 36$

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

Cancel the common factor.

$3 x + 2 \cdot (2 (\frac{- x}{2})) + 4 \cdot 8 = 36$

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

Rewrite the expression.

$3 x + 2 (- x) + 4 \cdot 8 = 36$

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

$3 x + 2 (- x) + 4 \cdot 8 = 36$

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

Multiply $- 1$ by $2$ .

$3 x - 2 x + 4 \cdot 8 = 36$

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

Multiply $4$ by $8$ .

$3 x - 2 x + 32 = 36$

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

$3 x - 2 x + 32 = 36$

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

Subtract $2 x$ from $3 x$ .

$x + 32 = 36$

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

$x + 32 = 36$

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

$x + 32 = 36$

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

$x + 32 = 36$

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

Step 3

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

Subtract $32$ from both sides of the equation.

$x = 36 - 32$

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

Subtract $32$ from $36$ .

$x = 4$

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

$x = 4$

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

Step 4

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

Replace all occurrences of $x$ in $y = - \frac{x}{2} + 8$ with $4$ .

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

$x = 4$

Simplify the right side.

Simplify $- \frac{4}{2} + 8$ .

Simplify each term.

Divide $4$ by $2$ .

$y = - 1 \cdot 2 + 8$

$x = 4$

Multiply $- 1$ by $2$ .

$y = - 2 + 8$

$x = 4$

$y = - 2 + 8$

$x = 4$

Add $- 2$ and $8$ .

$y = 6$

$x = 4$

$y = 6$

$x = 4$

$y = 6$

$x = 4$

$y = 6$

$x = 4$

Step 5

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

$(4, 6)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(4, 6)$

Equation Form:

$x = 4, y = 6$

Step 7

Solve the System of Equations 3x+4y=36 y=-1/2x+8

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