Solve by Substitution 2x+y=8 , y=x-7

$2 x + y = 8$ , $y = x - 7$

Step 1

Replace all occurrences of $y$ with $x - 7$ in each equation.

Replace all occurrences of $y$ in $2 x + y = 8$ with $x - 7$ .

$2 x + x - 7 = 8$

$y = x - 7$

Simplify the left side.

Simplify $2 x + x - 7$ .

Remove parentheses.

$2 x + x - 7 = 8$

$y = x - 7$

Add $2 x$ and $x$ .

$3 x - 7 = 8$

$y = x - 7$

$3 x - 7 = 8$

$y = x - 7$

$3 x - 7 = 8$

$y = x - 7$

$3 x - 7 = 8$

$y = x - 7$

Step 2

Solve for $x$ in $3 x - 7 = 8$ .

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

Add $7$ to both sides of the equation.

$3 x = 8 + 7$

$y = x - 7$

Add $8$ and $7$ .

$3 x = 15$

$y = x - 7$

$3 x = 15$

$y = x - 7$

Divide each term in $3 x = 15$ by $3$ and simplify.

Divide each term in $3 x = 15$ by $3$ .

$\frac{3 x}{3} = \frac{15}{3}$

$y = x - 7$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{15}{3}$

$y = x - 7$

Divide $x$ by $1$ .

$x = \frac{15}{3}$

$y = x - 7$

$x = \frac{15}{3}$

$y = x - 7$

$x = \frac{15}{3}$

$y = x - 7$

Simplify the right side.

Divide $15$ by $3$ .

$x = 5$

$y = x - 7$

$x = 5$

$y = x - 7$

$x = 5$

$y = x - 7$

$x = 5$

$y = x - 7$

Step 3

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

Replace all occurrences of $x$ in $y = x - 7$ with $5$ .

$y = (5) - 7$

$x = 5$

Simplify the right side.

Subtract $7$ from $5$ .

$y = - 2$

$x = 5$

$y = - 2$

$x = 5$

$y = - 2$

$x = 5$

Step 4

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

$(5, - 2)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(5, - 2)$

Equation Form:

$x = 5, y = - 2$

Step 6

Solve by Substitution 2x+y=8 , y=x-7

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