Solve by Substitution y=5x-3 and -x-5y=-11

$y = 5 x - 3$ and $- x - 5 y = - 11$

Replace all occurrences of $y$ with $5 x - 3$ in each equation.

Replace all occurrences of $y$ in $- x - 5 y = - 11$ with $5 x - 3$ .

$- x - 5 (5 x - 3) = - 11$

$y = 5 x - 3$

Simplify the left side.

Simplify $- x - 5 (5 x - 3)$ .

Simplify each term.

Apply the distributive property.

$- x - 5 (5 x) - 5 \cdot - 3 = - 11$

$y = 5 x - 3$

Multiply $5$ by $- 5$ .

$- x - 25 x - 5 \cdot - 3 = - 11$

$y = 5 x - 3$

Multiply $- 5$ by $- 3$ .

$- x - 25 x + 15 = - 11$

$y = 5 x - 3$

$- x - 25 x + 15 = - 11$

$y = 5 x - 3$

Subtract $25 x$ from $- x$ .

$- 26 x + 15 = - 11$

$y = 5 x - 3$

$- 26 x + 15 = - 11$

$y = 5 x - 3$

$- 26 x + 15 = - 11$

$y = 5 x - 3$

$- 26 x + 15 = - 11$

$y = 5 x - 3$

Solve for $x$ in $- 26 x + 15 = - 11$ .

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

Subtract $15$ from both sides of the equation.

$- 26 x = - 11 - 15$

$y = 5 x - 3$

Subtract $15$ from $- 11$ .

$- 26 x = - 26$

$y = 5 x - 3$

$- 26 x = - 26$

$y = 5 x - 3$

Divide each term in $- 26 x = - 26$ by $- 26$ and simplify.

Divide each term in $- 26 x = - 26$ by $- 26$ .

$\frac{- 26 x}{- 26} = \frac{- 26}{- 26}$

$y = 5 x - 3$

Simplify the left side.

Cancel the common factor of $- 26$ .

Cancel the common factor.

$\frac{- 26 x}{- 26} = \frac{- 26}{- 26}$

$y = 5 x - 3$

Divide $x$ by $1$ .

$x = \frac{- 26}{- 26}$

$y = 5 x - 3$

$x = \frac{- 26}{- 26}$

$y = 5 x - 3$

$x = \frac{- 26}{- 26}$

$y = 5 x - 3$

Simplify the right side.

Divide $- 26$ by $- 26$ .

$x = 1$

$y = 5 x - 3$

$x = 1$

$y = 5 x - 3$

$x = 1$

$y = 5 x - 3$

$x = 1$

$y = 5 x - 3$

Replace all occurrences of $x$ with $1$ in each equation.

Replace all occurrences of $x$ in $y = 5 x - 3$ with $1$ .

$y = 5 (1) - 3$

$x = 1$

Simplify the right side.

Simplify $5 (1) - 3$ .

Multiply $5$ by $1$ .

$y = 5 - 3$

$x = 1$

Subtract $3$ from $5$ .

$y = 2$

$x = 1$

$y = 2$

$x = 1$

$y = 2$

$x = 1$

$y = 2$

$x = 1$

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

$(1, 2)$

The result can be shown in multiple forms.

Point Form:

$(1, 2)$

Equation Form:

$x = 1, y = 2$

Solve by Substitution y=5x-3 and -x-5y=-11

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