Solve by Substitution y=4x+2 and y=3x+1

$y = 4 x + 2$ and $y = 3 x + 1$

Step 1

Eliminate the equal sides of each equation and combine.

$4 x + 2 = 3 x + 1$

Step 2

Solve $4 x + 2 = 3 x + 1$ for $x$ .

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

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

$4 x + 2 - 3 x = 1$

Subtract $3 x$ from $4 x$ .

$x + 2 = 1$

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

Subtract $2$ from both sides of the equation.

$x = 1 - 2$

Subtract $2$ from $1$ .

$x = - 1$

Step 3

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

Substitute $- 1$ for $x$ .

$y = 3 (- 1) + 1$

Simplify $3 (- 1) + 1$ .

Multiply $3$ by $- 1$ .

$y = - 3 + 1$

Add $- 3$ and $1$ .

$y = - 2$

Step 4

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

$(- 1, - 2)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 1, - 2)$

Equation Form:

$x = - 1, y = - 2$

Step 6