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

$y = x - 2$ $y = 3 x + 4$

Step 1

Eliminate the equal sides of each equation and combine.

$x - 2 = 3 x + 4$

Step 2

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

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

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

$x - 2 - 3 x = 4$

Subtract $3 x$ from $x$ .

$- 2 x - 2 = 4$

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

Add $2$ to both sides of the equation.

$- 2 x = 4 + 2$

Add $4$ and $2$ .

$- 2 x = 6$

Divide each term in $- 2 x = 6$ by $- 2$ and simplify.

Divide each term in $- 2 x = 6$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{6}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{6}{- 2}$

Divide $x$ by $1$ .

$x = \frac{6}{- 2}$

Simplify the right side.

Divide $6$ by $- 2$ .

$x = - 3$

Step 3

Evaluate $y$ when $x = - 3$ .

Substitute $- 3$ for $x$ .

$y = 3 (- 3) + 4$

Simplify $3 (- 3) + 4$ .

Multiply $3$ by $- 3$ .

$y = - 9 + 4$

Add $- 9$ and $4$ .

$y = - 5$

Step 4

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

$(- 3, - 5)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 3, - 5)$

Equation Form:

$x = - 3, y = - 5$

Step 6

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

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