Solve the System of Equations 2x+y=8 y=-x+5

$2 x + y = 8$ $y = - x + 5$

Step 1

Replace all occurrences of $y$ with $- x + 5$ in each equation.

Replace all occurrences of $y$ in $2 x + y = 8$ with $- x + 5$ .

$2 x - x + 5 = 8$

$y = - x + 5$

Simplify the left side.

Simplify $2 x - x + 5$ .

Remove parentheses.

$2 x - x + 5 = 8$

$y = - x + 5$

Subtract $x$ from $2 x$ .

$x + 5 = 8$

$y = - x + 5$

$x + 5 = 8$

$y = - x + 5$

$x + 5 = 8$

$y = - x + 5$

$x + 5 = 8$

$y = - x + 5$

Step 2

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

Subtract $5$ from both sides of the equation.

$x = 8 - 5$

$y = - x + 5$

Subtract $5$ from $8$ .

$x = 3$

$y = - x + 5$

$x = 3$

$y = - x + 5$

Step 3

Replace all occurrences of $x$ with $3$ in each equation.

Replace all occurrences of $x$ in $y = - x + 5$ with $3$ .

$y = - (3) + 5$

$x = 3$

Simplify the right side.

Simplify $- (3) + 5$ .

Multiply $- 1$ by $3$ .

$y = - 3 + 5$

$x = 3$

Add $- 3$ and $5$ .

$y = 2$

$x = 3$

$y = 2$

$x = 3$

$y = 2$

$x = 3$

$y = 2$

$x = 3$

Step 4

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

$(3, 2)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(3, 2)$

Equation Form:

$x = 3, y = 2$

Step 6

Solve the System of Equations 2x+y=8 y=-x+5

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