Solve the System of Equations y=4x+25 y=9x

$y = 4 x + 25$ $y = 9 x$

Step 1

Eliminate the equal sides of each equation and combine.

$4 x + 25 = 9 x$

Step 2

Solve $4 x + 25 = 9 x$ for $x$ .

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

Subtract $9 x$ from both sides of the equation.

$4 x + 25 - 9 x = 0$

Subtract $9 x$ from $4 x$ .

$- 5 x + 25 = 0$

Subtract $25$ from both sides of the equation.

$- 5 x = - 25$

Divide each term in $- 5 x = - 25$ by $- 5$ and simplify.

Divide each term in $- 5 x = - 25$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{- 25}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{- 25}{- 5}$

Divide $x$ by $1$ .

$x = \frac{- 25}{- 5}$

Simplify the right side.

Divide $- 25$ by $- 5$ .

$x = 5$

Step 3

Evaluate $y$ when $x = 5$ .

Substitute $5$ for $x$ .

$y = 9 (5)$

Multiply $9$ by $5$ .

$y = 45$

Step 4

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

$(5, 45)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(5, 45)$

Equation Form:

$x = 5, y = 45$

Step 6