Solve by Substitution y=-x+5 , x-4y=10

$y = - x + 5$ , $x - 4 y = 10$

Step 1

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

Replace all occurrences of $y$ in $x - 4 y = 10$ with $- x + 5$ .

$x - 4 (- x + 5) = 10$

$y = - x + 5$

Simplify the left side.

Simplify $x - 4 (- x + 5)$ .

Simplify each term.

Apply the distributive property.

$x - 4 (- x) - 4 \cdot 5 = 10$

$y = - x + 5$

Multiply $- 1$ by $- 4$ .

$x + 4 x - 4 \cdot 5 = 10$

$y = - x + 5$

Multiply $- 4$ by $5$ .

$x + 4 x - 20 = 10$

$y = - x + 5$

$x + 4 x - 20 = 10$

$y = - x + 5$

Add $x$ and $4 x$ .

$5 x - 20 = 10$

$y = - x + 5$

$5 x - 20 = 10$

$y = - x + 5$

$5 x - 20 = 10$

$y = - x + 5$

$5 x - 20 = 10$

$y = - x + 5$

Step 2

Solve for $x$ in $5 x - 20 = 10$ .

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

Add $20$ to both sides of the equation.

$5 x = 10 + 20$

$y = - x + 5$

Add $10$ and $20$ .

$5 x = 30$

$y = - x + 5$

$5 x = 30$

$y = - x + 5$

Divide each term in $5 x = 30$ by $5$ and simplify.

Divide each term in $5 x = 30$ by $5$ .

$\frac{5 x}{5} = \frac{30}{5}$

$y = - x + 5$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{30}{5}$

$y = - x + 5$

Divide $x$ by $1$ .

$x = \frac{30}{5}$

$y = - x + 5$

$x = \frac{30}{5}$

$y = - x + 5$

$x = \frac{30}{5}$

$y = - x + 5$

Simplify the right side.

Divide $30$ by $5$ .

$x = 6$

$y = - x + 5$

$x = 6$

$y = - x + 5$

$x = 6$

$y = - x + 5$

$x = 6$

$y = - x + 5$

Step 3

Replace all occurrences of $x$ with $6$ in each equation.

Replace all occurrences of $x$ in $y = - x + 5$ with $6$ .

$y = - (6) + 5$

$x = 6$

Simplify the right side.

Simplify $- (6) + 5$ .

Multiply $- 1$ by $6$ .

$y = - 6 + 5$

$x = 6$

Add $- 6$ and $5$ .

$y = - 1$

$x = 6$

$y = - 1$

$x = 6$

$y = - 1$

$x = 6$

$y = - 1$

$x = 6$

Step 4

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

$(6, - 1)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(6, - 1)$

Equation Form:

$x = 6, y = - 1$

Step 6

Solve by Substitution y=-x+5 , x-4y=10

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