Solve the System of Equations 4x+4y=4 3x+4y=10

$4 x + 4 y = 4$ $3 x + 4 y = 10$

Step 1

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

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

$4 x = 4 - 4 y$

$3 x + 4 y = 10$

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

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

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

$3 x + 4 y = 10$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

$3 x + 4 y = 10$

Divide $x$ by $1$ .

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

$3 x + 4 y = 10$

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

$3 x + 4 y = 10$

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

$3 x + 4 y = 10$

Simplify the right side.

Simplify each term.

Divide $4$ by $4$ .

$x = 1 + \frac{- 4 y}{4}$

$3 x + 4 y = 10$

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

Factor $4$ out of $- 4 y$ .

$x = 1 + \frac{4 (- y)}{4}$

$3 x + 4 y = 10$

Cancel the common factors.

Factor $4$ out of $4$ .

$x = 1 + \frac{4 (- y)}{4 (1)}$

$3 x + 4 y = 10$

Cancel the common factor.

$x = 1 + \frac{4 (- y)}{4 \cdot 1}$

$3 x + 4 y = 10$

Rewrite the expression.

$x = 1 + \frac{- y}{1}$

$3 x + 4 y = 10$

Divide $- y$ by $1$ .

$x = 1 - y$

$3 x + 4 y = 10$

$x = 1 - y$

$3 x + 4 y = 10$

$x = 1 - y$

$3 x + 4 y = 10$

$x = 1 - y$

$3 x + 4 y = 10$

$x = 1 - y$

$3 x + 4 y = 10$

$x = 1 - y$

$3 x + 4 y = 10$

$x = 1 - y$

$3 x + 4 y = 10$

Step 2

Replace all occurrences of $x$ with $1 - y$ in each equation.

Replace all occurrences of $x$ in $3 x + 4 y = 10$ with $1 - y$ .

$3 (1 - y) + 4 y = 10$

$x = 1 - y$

Simplify the left side.

Simplify $3 (1 - y) + 4 y$ .

Simplify each term.

Apply the distributive property.

$3 \cdot 1 + 3 (- y) + 4 y = 10$

$x = 1 - y$

Multiply $3$ by $1$ .

$3 + 3 (- y) + 4 y = 10$

$x = 1 - y$

Multiply $- 1$ by $3$ .

$3 - 3 y + 4 y = 10$

$x = 1 - y$

$3 - 3 y + 4 y = 10$

$x = 1 - y$

Add $- 3 y$ and $4 y$ .

$3 + y = 10$

$x = 1 - y$

$3 + y = 10$

$x = 1 - y$

$3 + y = 10$

$x = 1 - y$

$3 + y = 10$

$x = 1 - y$

Step 3

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

Subtract $3$ from both sides of the equation.

$y = 10 - 3$

$x = 1 - y$

Subtract $3$ from $10$ .

$y = 7$

$x = 1 - y$

$y = 7$

$x = 1 - y$

Step 4

Replace all occurrences of $y$ with $7$ in each equation.

Replace all occurrences of $y$ in $x = 1 - y$ with $7$ .

$x = 1 - (7)$

$y = 7$

Simplify the right side.

Simplify $1 - (7)$ .

Multiply $- 1$ by $7$ .

$x = 1 - 7$

$y = 7$

Subtract $7$ from $1$ .

$x = - 6$

$y = 7$

$x = - 6$

$y = 7$

$x = - 6$

$y = 7$

$x = - 6$

$y = 7$

Step 5

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

$(- 6, 7)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 6, 7)$

Equation Form:

$x = - 6, y = 7$

Step 7

Solve the System of Equations 4x+4y=4 3x+4y=10

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