Solve the System of Equations x+y=4 and 3x+7y=32

$x + y = 4$ and $3 x + 7 y = 32$

Step 1

Subtract $y$ from both sides of the equation.

$x = 4 - y$

$3 x + 7 y = 32$

Step 2

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

Replace all occurrences of $x$ in $3 x + 7 y = 32$ with $4 - y$ .

$3 (4 - y) + 7 y = 32$

$x = 4 - y$

Simplify the left side.

Simplify $3 (4 - y) + 7 y$ .

Simplify each term.

Apply the distributive property.

$3 \cdot 4 + 3 (- y) + 7 y = 32$

$x = 4 - y$

Multiply $3$ by $4$ .

$12 + 3 (- y) + 7 y = 32$

$x = 4 - y$

Multiply $- 1$ by $3$ .

$12 - 3 y + 7 y = 32$

$x = 4 - y$

$12 - 3 y + 7 y = 32$

$x = 4 - y$

Add $- 3 y$ and $7 y$ .

$12 + 4 y = 32$

$x = 4 - y$

$12 + 4 y = 32$

$x = 4 - y$

$12 + 4 y = 32$

$x = 4 - y$

$12 + 4 y = 32$

$x = 4 - y$

Step 3

Solve for $y$ in $12 + 4 y = 32$ .

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

Subtract $12$ from both sides of the equation.

$4 y = 32 - 12$

$x = 4 - y$

Subtract $12$ from $32$ .

$4 y = 20$

$x = 4 - y$

$4 y = 20$

$x = 4 - y$

Divide each term in $4 y = 20$ by $4$ and simplify.

Divide each term in $4 y = 20$ by $4$ .

$\frac{4 y}{4} = \frac{20}{4}$

$x = 4 - y$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{20}{4}$

$x = 4 - y$

Divide $y$ by $1$ .

$y = \frac{20}{4}$

$x = 4 - y$

$y = \frac{20}{4}$

$x = 4 - y$

$y = \frac{20}{4}$

$x = 4 - y$

Simplify the right side.

Divide $20$ by $4$ .

$y = 5$

$x = 4 - y$

$y = 5$

$x = 4 - y$

$y = 5$

$x = 4 - y$

$y = 5$

$x = 4 - y$

Step 4

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

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

$x = 4 - (5)$

$y = 5$

Simplify the right side.

Simplify $4 - (5)$ .

Multiply $- 1$ by $5$ .

$x = 4 - 5$

$y = 5$

Subtract $5$ from $4$ .

$x = - 1$

$y = 5$

$x = - 1$

$y = 5$

$x = - 1$

$y = 5$

$x = - 1$

$y = 5$

Step 5

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

$(- 1, 5)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 1, 5)$

Equation Form:

$x = - 1, y = 5$

Step 7

Solve the System of Equations x+y=4 and 3x+7y=32

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