Solve the System of Equations 3x+2y=4 2y=8-5x

$3 x + 2 y = 4$ $2 y = 8 - 5 x$

Step 1

Divide each term in $2 y = 8 - 5 x$ by $2$ and simplify.

Divide each term in $2 y = 8 - 5 x$ by $2$ .

$\frac{2 y}{2} = \frac{8}{2} + \frac{- 5 x}{2}$

$3 x + 2 y = 4$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{8}{2} + \frac{- 5 x}{2}$

$3 x + 2 y = 4$

Divide $y$ by $1$ .

$y = \frac{8}{2} + \frac{- 5 x}{2}$

$3 x + 2 y = 4$

$y = \frac{8}{2} + \frac{- 5 x}{2}$

$3 x + 2 y = 4$

$y = \frac{8}{2} + \frac{- 5 x}{2}$

$3 x + 2 y = 4$

Simplify the right side.

Simplify each term.

Divide $8$ by $2$ .

$y = 4 + \frac{- 5 x}{2}$

$3 x + 2 y = 4$

Move the negative in front of the fraction.

$y = 4 - \frac{5 x}{2}$

$3 x + 2 y = 4$

$y = 4 - \frac{5 x}{2}$

$3 x + 2 y = 4$

$y = 4 - \frac{5 x}{2}$

$3 x + 2 y = 4$

$y = 4 - \frac{5 x}{2}$

$3 x + 2 y = 4$

Step 2

Replace all occurrences of $y$ with $4 - \frac{5 x}{2}$ in each equation.

Replace all occurrences of $y$ in $3 x + 2 y = 4$ with $4 - \frac{5 x}{2}$ .

$3 x + 2 (4 - \frac{5 x}{2}) = 4$

$y = 4 - \frac{5 x}{2}$

Simplify the left side.

Simplify $3 x + 2 (4 - \frac{5 x}{2})$ .

Simplify each term.

Apply the distributive property.

$3 x + 2 \cdot 4 + 2 (- \frac{5 x}{2}) = 4$

$y = 4 - \frac{5 x}{2}$

Multiply $2$ by $4$ .

$3 x + 8 + 2 (- \frac{5 x}{2}) = 4$

$y = 4 - \frac{5 x}{2}$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{5 x}{2}$ into the numerator.

$3 x + 8 + 2 (\frac{- 5 x}{2}) = 4$

$y = 4 - \frac{5 x}{2}$

Cancel the common factor.

$3 x + 8 + 2 (\frac{- 5 x}{2}) = 4$

$y = 4 - \frac{5 x}{2}$

Rewrite the expression.

$3 x + 8 - 5 x = 4$

$y = 4 - \frac{5 x}{2}$

$3 x + 8 - 5 x = 4$

$y = 4 - \frac{5 x}{2}$

$3 x + 8 - 5 x = 4$

$y = 4 - \frac{5 x}{2}$

Subtract $5 x$ from $3 x$ .

$- 2 x + 8 = 4$

$y = 4 - \frac{5 x}{2}$

$- 2 x + 8 = 4$

$y = 4 - \frac{5 x}{2}$

$- 2 x + 8 = 4$

$y = 4 - \frac{5 x}{2}$

$- 2 x + 8 = 4$

$y = 4 - \frac{5 x}{2}$

Step 3

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

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

Subtract $8$ from both sides of the equation.

$- 2 x = 4 - 8$

$y = 4 - \frac{5 x}{2}$

Subtract $8$ from $4$ .

$- 2 x = - 4$

$y = 4 - \frac{5 x}{2}$

$- 2 x = - 4$

$y = 4 - \frac{5 x}{2}$

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

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

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

$y = 4 - \frac{5 x}{2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

$y = 4 - \frac{5 x}{2}$

Divide $x$ by $1$ .

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

$y = 4 - \frac{5 x}{2}$

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

$y = 4 - \frac{5 x}{2}$

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

$y = 4 - \frac{5 x}{2}$

Simplify the right side.

Divide $- 4$ by $- 2$ .

$x = 2$

$y = 4 - \frac{5 x}{2}$

$x = 2$

$y = 4 - \frac{5 x}{2}$

$x = 2$

$y = 4 - \frac{5 x}{2}$

$x = 2$

$y = 4 - \frac{5 x}{2}$

Step 4

Replace all occurrences of $x$ with $2$ in each equation.

Replace all occurrences of $x$ in $y = 4 - \frac{5 x}{2}$ with $2$ .

$y = 4 - \frac{5 (2)}{2}$

$x = 2$

Simplify the right side.

Simplify $4 - \frac{5 (2)}{2}$ .

Simplify each term.

Cancel the common factor of $2$ .

Cancel the common factor.

$y = 4 - \frac{5 \cdot 2}{2}$

$x = 2$

Divide $5$ by $1$ .

$y = 4 - 1 \cdot 5$

$x = 2$

$y = 4 - 1 \cdot 5$

$x = 2$

Multiply $- 1$ by $5$ .

$y = 4 - 5$

$x = 2$

$y = 4 - 5$

$x = 2$

Subtract $5$ from $4$ .

$y = - 1$

$x = 2$

$y = - 1$

$x = 2$

$y = - 1$

$x = 2$

$y = - 1$

$x = 2$

Step 5

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

$(2, - 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(2, - 1)$

Equation Form:

$x = 2, y = - 1$

Step 7

Solve the System of Equations 3x+2y=4 2y=8-5x

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