Solve the System of Equations Solve the system of equations y=3x+4 and y=2x+4 using the Graphing Method.

Solve the system of equations $y = 3 x + 4$ and $y = 2 x + 4$ using the Graphing Method.

Step 1

Eliminate the equal sides of each equation and combine.

$3 x + 4 = 2 x + 4$

Step 2

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

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

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

$3 x + 4 - 2 x = 4$

Subtract $2 x$ from $3 x$ .

$x + 4 = 4$

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

Subtract $4$ from both sides of the equation.

$x = 4 - 4$

Subtract $4$ from $4$ .

$x = 0$

Step 3

Evaluate $y$ when $x = 0$ .

Substitute $0$ for $x$ .

$y = 2 (0) + 4$

Simplify $2 (0) + 4$ .

Multiply $2$ by $0$ .

$y = 0 + 4$

Add $0$ and $4$ .

$y = 4$

Step 4

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

$(0, 4)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(0, 4)$

Equation Form:

$x = 0, y = 4$

Step 6