Solve the System of Equations y=x+2 y=3x-2

$y = x + 2$ $y = 3 x - 2$

Step 1

Eliminate the equal sides of each equation and combine.

$x + 2 = 3 x - 2$

Step 2

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

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

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

$x + 2 - 3 x = - 2$

Subtract $3 x$ from $x$ .

$- 2 x + 2 = - 2$

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

Subtract $2$ from both sides of the equation.

$- 2 x = - 2 - 2$

Subtract $2$ from $- 2$ .

$- 2 x = - 4$

Divide each term in $- 2 x = - 4$ by $- 2$ and simplify.

Divide each term in $- 2 x = - 4$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 4}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 4}{- 2}$

Divide $x$ by $1$ .

$x = \frac{- 4}{- 2}$

Simplify the right side.

Divide $- 4$ by $- 2$ .

$x = 2$

Step 3

Evaluate $y$ when $x = 2$ .

Substitute $2$ for $x$ .

$y = 3 (2) - 2$

Simplify $3 (2) - 2$ .

Multiply $3$ by $2$ .

$y = 6 - 2$

Subtract $2$ from $6$ .

$y = 4$

Step 4

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

$(2, 4)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(2, 4)$

Equation Form:

$x = 2, y = 4$

Step 6

Solve the System of Equations y=x+2 y=3x-2

Related Questions

Support LCMGCF.com by disabling your adblocker.