Solve the System of Equations y=-2x+19 y=x+7

$y = - 2 x + 19$ $y = x + 7$

Step 1

Eliminate the equal sides of each equation and combine.

$- 2 x + 19 = x + 7$

Step 2

Solve $- 2 x + 19 = x + 7$ for $x$ .

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

Subtract $x$ from both sides of the equation.

$- 2 x + 19 - x = 7$

Subtract $x$ from $- 2 x$ .

$- 3 x + 19 = 7$

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

Subtract $19$ from both sides of the equation.

$- 3 x = 7 - 19$

Subtract $19$ from $7$ .

$- 3 x = - 12$

Divide each term in $- 3 x = - 12$ by $- 3$ and simplify.

Divide each term in $- 3 x = - 12$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{- 12}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{- 12}{- 3}$

Divide $x$ by $1$ .

$x = \frac{- 12}{- 3}$

Simplify the right side.

Divide $- 12$ by $- 3$ .

$x = 4$

Step 3

Evaluate $y$ when $x = 4$ .

Substitute $4$ for $x$ .

$y = (4) + 7$

Substitute $4$ for $x$ in $y = (4) + 7$ and solve for $y$ .

Remove parentheses.

$y = 4 + 7$

Remove parentheses.

$y = (4) + 7$

Add $4$ and $7$ .

$y = 11$

Step 4

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

$(4, 11)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(4, 11)$

Equation Form:

$x = 4, y = 11$

Step 6

Solve the System of Equations y=-2x+19 y=x+7

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