Solve the System of Equations y=3x+5 and y=2x+4

$y = 3 x + 5$ and $y = 2 x + 4$

Eliminate the equal sides of each equation and combine.

$3 x + 5 = 2 x + 4$

Solve $3 x + 5 = 2 x + 4$ for $x$ .

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

Subtract $2 x$ from both sides of the equation.

$3 x + 5 - 2 x = 4$

Subtract $2 x$ from $3 x$ .

$x + 5 = 4$

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

Subtract $5$ from both sides of the equation.

$x = 4 - 5$

Subtract $5$ from $4$ .

$x = - 1$

Evaluate $y$ when $x = - 1$ .

Substitute $- 1$ for $x$ .

$y = 2 (- 1) + 4$

Simplify $2 (- 1) + 4$ .

Multiply $2$ by $- 1$ .

$y = - 2 + 4$

Add $- 2$ and $4$ .

$y = 2$

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

$(- 1, 2)$

The result can be shown in multiple forms.

Point Form:

$(- 1, 2)$

Equation Form:

$x = - 1, y = 2$