Solve the System of Equations y=x+5 and y=5x+5

$y = x + 5$ and $y = 5 x + 5$

Step 1

Eliminate the equal sides of each equation and combine.

$x + 5 = 5 x + 5$

Step 2

Solve $x + 5 = 5 x + 5$ for $x$ .

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

Subtract $5 x$ from both sides of the equation.

$x + 5 - 5 x = 5$

Subtract $5 x$ from $x$ .

$- 4 x + 5 = 5$

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

Subtract $5$ from both sides of the equation.

$- 4 x = 5 - 5$

Subtract $5$ from $5$ .

$- 4 x = 0$

Divide each term in $- 4 x = 0$ by $- 4$ and simplify.

Divide each term in $- 4 x = 0$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{0}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{0}{- 4}$

Divide $x$ by $1$ .

$x = \frac{0}{- 4}$

Simplify the right side.

Divide $0$ by $- 4$ .

$x = 0$

Step 3

Evaluate $y$ when $x = 0$ .

Substitute $0$ for $x$ .

$y = 5 (0) + 5$

Simplify $5 (0) + 5$ .

Multiply $5$ by $0$ .

$y = 0 + 5$

Add $0$ and $5$ .

$y = 5$

Step 4

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

$(0, 5)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(0, 5)$

Equation Form:

$x = 0, y = 5$

Step 6

Solve the System of Equations y=x+5 and y=5x+5

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