Solve the System of Equations y=7x y=3x+20

$y = 7 x$ $y = 3 x + 20$

Step 1

Eliminate the equal sides of each equation and combine.

$7 x = 3 x + 20$

Step 2

Solve $7 x = 3 x + 20$ for $x$ .

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

Subtract $3 x$ from both sides of the equation.

$7 x - 3 x = 20$

Subtract $3 x$ from $7 x$ .

$4 x = 20$

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

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

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $20$ by $4$ .

$x = 5$

Step 3

Evaluate $y$ when $x = 5$ .

Substitute $5$ for $x$ .

$y = 3 (5) + 20$

Simplify $3 (5) + 20$ .

Multiply $3$ by $5$ .

$y = 15 + 20$

Add $15$ and $20$ .

$y = 35$

Step 4

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

$(5, 35)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(5, 35)$

Equation Form:

$x = 5, y = 35$

Step 6