Solve by Substitution 5x-2y=-1 , x+4y=35

$5 x - 2 y = - 1$ , $x + 4 y = 35$

Step 1

Subtract $4 y$ from both sides of the equation.

$x = 35 - 4 y$

$5 x - 2 y = - 1$

Step 2

Replace all occurrences of $x$ with $35 - 4 y$ in each equation.

Replace all occurrences of $x$ in $5 x - 2 y = - 1$ with $35 - 4 y$ .

$5 (35 - 4 y) - 2 y = - 1$

$x = 35 - 4 y$

Simplify the left side.

Simplify $5 (35 - 4 y) - 2 y$ .

Simplify each term.

Apply the distributive property.

$5 \cdot 35 + 5 (- 4 y) - 2 y = - 1$

$x = 35 - 4 y$

Multiply $5$ by $35$ .

$175 + 5 (- 4 y) - 2 y = - 1$

$x = 35 - 4 y$

Multiply $- 4$ by $5$ .

$175 - 20 y - 2 y = - 1$

$x = 35 - 4 y$

$175 - 20 y - 2 y = - 1$

$x = 35 - 4 y$

Subtract $2 y$ from $- 20 y$ .

$175 - 22 y = - 1$

$x = 35 - 4 y$

$175 - 22 y = - 1$

$x = 35 - 4 y$

$175 - 22 y = - 1$

$x = 35 - 4 y$

$175 - 22 y = - 1$

$x = 35 - 4 y$

Step 3

Solve for $y$ in $175 - 22 y = - 1$ .

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

Subtract $175$ from both sides of the equation.

$- 22 y = - 1 - 175$

$x = 35 - 4 y$

Subtract $175$ from $- 1$ .

$- 22 y = - 176$

$x = 35 - 4 y$

$- 22 y = - 176$

$x = 35 - 4 y$

Divide each term in $- 22 y = - 176$ by $- 22$ and simplify.

Divide each term in $- 22 y = - 176$ by $- 22$ .

$\frac{- 22 y}{- 22} = \frac{- 176}{- 22}$

$x = 35 - 4 y$

Simplify the left side.

Cancel the common factor of $- 22$ .

Cancel the common factor.

$\frac{- 22 y}{- 22} = \frac{- 176}{- 22}$

$x = 35 - 4 y$

Divide $y$ by $1$ .

$y = \frac{- 176}{- 22}$

$x = 35 - 4 y$

$y = \frac{- 176}{- 22}$

$x = 35 - 4 y$

$y = \frac{- 176}{- 22}$

$x = 35 - 4 y$

Simplify the right side.

Divide $- 176$ by $- 22$ .

$y = 8$

$x = 35 - 4 y$

$y = 8$

$x = 35 - 4 y$

$y = 8$

$x = 35 - 4 y$

$y = 8$

$x = 35 - 4 y$

Step 4

Replace all occurrences of $y$ with $8$ in each equation.

Replace all occurrences of $y$ in $x = 35 - 4 y$ with $8$ .

$x = 35 - 4 \cdot 8$

$y = 8$

Simplify the right side.

Simplify $35 - 4 \cdot 8$ .

Multiply $- 4$ by $8$ .

$x = 35 - 32$

$y = 8$

Subtract $32$ from $35$ .

$x = 3$

$y = 8$

$x = 3$

$y = 8$

$x = 3$

$y = 8$

$x = 3$

$y = 8$

Step 5

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

$(3, 8)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(3, 8)$

Equation Form:

$x = 3, y = 8$

Step 7

Solve by Substitution 5x-2y=-1 , x+4y=35

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