Solve in Terms of the Arbitrary Variable y 4x-5y=1 -8x+10y=-2

$4 x - 5 y = 1$ $- 8 x + 10 y = - 2$

Step 1

Simplify the right side.

Simplify $\frac{1}{4} + \frac{5 (- \frac{1}{5} + \frac{4 x}{5})}{4}$ .

Combine the numerators over the common denominator.

$x = \frac{1 + 5 (- \frac{1}{5} + \frac{4 x}{5})}{4}$

$y = - \frac{1}{5} + \frac{4 x}{5}$

Simplify each term.

Apply the distributive property.

$x = \frac{1 + 5 (- \frac{1}{5}) + 5 (\frac{4 x}{5})}{4}$

$y = - \frac{1}{5} + \frac{4 x}{5}$

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{1}{5}$ into the numerator.

$x = \frac{1 + 5 (\frac{- 1}{5}) + 5 (\frac{4 x}{5})}{4}$

$y = - \frac{1}{5} + \frac{4 x}{5}$

Cancel the common factor.

$x = \frac{1 + 5 (\frac{- 1}{5}) + 5 (\frac{4 x}{5})}{4}$

$y = - \frac{1}{5} + \frac{4 x}{5}$

Rewrite the expression.

$x = \frac{1 - 1 + 5 (\frac{4 x}{5})}{4}$

$y = - \frac{1}{5} + \frac{4 x}{5}$

$x = \frac{1 - 1 + 5 (\frac{4 x}{5})}{4}$

$y = - \frac{1}{5} + \frac{4 x}{5}$

Cancel the common factor of $5$ .

Cancel the common factor.

$x = \frac{1 - 1 + 5 (\frac{4 x}{5})}{4}$

$y = - \frac{1}{5} + \frac{4 x}{5}$

Rewrite the expression.

$x = \frac{1 - 1 + 4 x}{4}$

$y = - \frac{1}{5} + \frac{4 x}{5}$

$x = \frac{1 - 1 + 4 x}{4}$

$y = - \frac{1}{5} + \frac{4 x}{5}$

$x = \frac{1 - 1 + 4 x}{4}$

$y = - \frac{1}{5} + \frac{4 x}{5}$

Reduce the expression by cancelling the common factors.

Subtract $1$ from $1$ .

$x = \frac{0 + 4 x}{4}$

$y = - \frac{1}{5} + \frac{4 x}{5}$

Add $0$ and $4 x$ .

$x = \frac{4 x}{4}$

$y = - \frac{1}{5} + \frac{4 x}{5}$

Cancel the common factor of $4$ .

Cancel the common factor.

$x = \frac{4 x}{4}$

$y = - \frac{1}{5} + \frac{4 x}{5}$

Divide $x$ by $1$ .

$x = x$

$y = - \frac{1}{5} + \frac{4 x}{5}$

$x = x$

$y = - \frac{1}{5} + \frac{4 x}{5}$

$x = x$

$y = - \frac{1}{5} + \frac{4 x}{5}$

$x = x$

$y = - \frac{1}{5} + \frac{4 x}{5}$

$x = x$

$y = - \frac{1}{5} + \frac{4 x}{5}$

Step 2

Simplify the right side.

Multiply $4$ by $x$ .

$y = - \frac{1}{5} + \frac{4 x}{5}$

$x = x$

$y = - \frac{1}{5} + \frac{4 x}{5}$

$x = x$

Step 3

Simplify the right side.

Reorder $- \frac{1}{5}$ and $\frac{4 x}{5}$ .

$y = \frac{4 x}{5} - \frac{1}{5}$

$x = x$

$y = \frac{4 x}{5} - \frac{1}{5}$

$x = x$

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