Solve the System of Equations y=x-2 y=-2x+7

$y = x - 2$ $y = - 2 x + 7$

Step 1

Eliminate the equal sides of each equation and combine.

$x - 2 = - 2 x + 7$

Step 2

Solve $x - 2 = - 2 x + 7$ for $x$ .

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

Add $2 x$ to both sides of the equation.

$x - 2 + 2 x = 7$

Add $x$ and $2 x$ .

$3 x - 2 = 7$

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

Add $2$ to both sides of the equation.

$3 x = 7 + 2$

Add $7$ and $2$ .

$3 x = 9$

Divide each term in $3 x = 9$ by $3$ and simplify.

Divide each term in $3 x = 9$ by $3$ .

$\frac{3 x}{3} = \frac{9}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{9}{3}$

Divide $x$ by $1$ .

$x = \frac{9}{3}$

Simplify the right side.

Divide $9$ by $3$ .

$x = 3$

Step 3

Evaluate $y$ when $x = 3$ .

Substitute $3$ for $x$ .

$y = - 2 \cdot 3 + 7$

Substitute $3$ for $x$ in $y = - 2 \cdot 3 + 7$ and solve for $y$ .

Remove parentheses.

$y = - 2 \cdot 3 + 7$

Simplify $- 2 \cdot 3 + 7$ .

Multiply $- 2$ by $3$ .

$y = - 6 + 7$

Add $- 6$ and $7$ .

$y = 1$

Step 4

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

$(3, 1)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(3, 1)$

Equation Form:

$x = 3, y = 1$

Step 6

Solve the System of Equations y=x-2 y=-2x+7

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