Solve the System of Equations y=1/4x+1 y=-x-9

$y = \frac{1}{4} x + 1$ $y = - x - 9$

Step 1

Eliminate the equal sides of each equation and combine.

$\frac{1}{4} x + 1 = - x - 9$

Step 2

Solve $\frac{1}{4} x + 1 = - x - 9$ for $x$ .

Combine $\frac{1}{4}$ and $x$ .

$\frac{x}{4} + 1 = - x - 9$

Move all terms containing $x$ to the left side of the equation.

Add $x$ to both sides of the equation.

$\frac{x}{4} + 1 + x = - 9$

To write $x$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{x}{4} + x \cdot \frac{4}{4} + 1 = - 9$

Combine $x$ and $\frac{4}{4}$ .

$\frac{x}{4} + \frac{x \cdot 4}{4} + 1 = - 9$

Combine the numerators over the common denominator.

$\frac{x + x \cdot 4}{4} + 1 = - 9$

Add $x$ and $x \cdot 4$ .

Reorder $x$ and $4$ .

$\frac{x + 4 \cdot x}{4} + 1 = - 9$

Add $x$ and $4 \cdot x$ .

$\frac{5 x}{4} + 1 = - 9$

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

Subtract $1$ from both sides of the equation.

$\frac{5 x}{4} = - 9 - 1$

Subtract $1$ from $- 9$ .

$\frac{5 x}{4} = - 10$

Multiply both sides of the equation by $\frac{4}{5}$ .

$\frac{4}{5} \cdot \frac{5 x}{4} = \frac{4}{5} \cdot - 10$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{4}{5} \cdot \frac{5 x}{4}$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4}{5} \cdot \frac{5 x}{4} = \frac{4}{5} \cdot - 10$

Rewrite the expression.

$\frac{1}{5} (5 x) = \frac{4}{5} \cdot - 10$

Cancel the common factor of $5$ .

Factor $5$ out of $5 x$ .

$\frac{1}{5} (5 (x)) = \frac{4}{5} \cdot - 10$

Cancel the common factor.

$\frac{1}{5} (5 x) = \frac{4}{5} \cdot - 10$

Rewrite the expression.

$x = \frac{4}{5} \cdot - 10$

Simplify the right side.

Simplify $\frac{4}{5} \cdot - 10$ .

Cancel the common factor of $5$ .

Factor $5$ out of $- 10$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x = 4 \cdot - 2$

Multiply $4$ by $- 2$ .

$x = - 8$

Step 3

Evaluate $y$ when $x = - 8$ .

Substitute $- 8$ for $x$ .

$y = - (- 8) - 9$

Simplify $- (- 8) - 9$ .

Multiply $- 1$ by $- 8$ .

$y = 8 - 9$

Subtract $9$ from $8$ .

$y = - 1$

Step 4

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

$(- 8, - 1)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 8, - 1)$

Equation Form:

$x = - 8, y = - 1$

Step 6

Solve the System of Equations y=1/4x+1 y=-x-9

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