Solve by Substitution 4x+5y=2 , 8x+10y=4

$4 x + 5 y = 2$ , $8 x + 10 y = 4$

Step 1

Solve for $x$ in $4 x + 5 y = 2$ .

Subtract $5 y$ from both sides of the equation.

$4 x = 2 - 5 y$

$8 x + 10 y = 4$

Divide each term in $4 x = 2 - 5 y$ by $4$ and simplify.

Divide each term in $4 x = 2 - 5 y$ by $4$ .

$\frac{4 x}{4} = \frac{2}{4} + \frac{- 5 y}{4}$

$8 x + 10 y = 4$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{2}{4} + \frac{- 5 y}{4}$

$8 x + 10 y = 4$

Divide $x$ by $1$ .

$x = \frac{2}{4} + \frac{- 5 y}{4}$

$8 x + 10 y = 4$

$x = \frac{2}{4} + \frac{- 5 y}{4}$

$8 x + 10 y = 4$

$x = \frac{2}{4} + \frac{- 5 y}{4}$

$8 x + 10 y = 4$

Simplify the right side.

Simplify each term.

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2$ .

$x = \frac{2 (1)}{4} + \frac{- 5 y}{4}$

$8 x + 10 y = 4$

Cancel the common factors.

Factor $2$ out of $4$ .

$x = \frac{2 \cdot 1}{2 \cdot 2} + \frac{- 5 y}{4}$

$8 x + 10 y = 4$

Cancel the common factor.

$x = \frac{2 \cdot 1}{2 \cdot 2} + \frac{- 5 y}{4}$

$8 x + 10 y = 4$

Rewrite the expression.

$x = \frac{1}{2} + \frac{- 5 y}{4}$

$8 x + 10 y = 4$

$x = \frac{1}{2} + \frac{- 5 y}{4}$

$8 x + 10 y = 4$

$x = \frac{1}{2} + \frac{- 5 y}{4}$

$8 x + 10 y = 4$

Move the negative in front of the fraction.

$x = \frac{1}{2} - \frac{5 y}{4}$

$8 x + 10 y = 4$

$x = \frac{1}{2} - \frac{5 y}{4}$

$8 x + 10 y = 4$

$x = \frac{1}{2} - \frac{5 y}{4}$

$8 x + 10 y = 4$

$x = \frac{1}{2} - \frac{5 y}{4}$

$8 x + 10 y = 4$

$x = \frac{1}{2} - \frac{5 y}{4}$

$8 x + 10 y = 4$

Step 2

Replace all occurrences of $x$ with $\frac{1}{2} - \frac{5 y}{4}$ in each equation.

Replace all occurrences of $x$ in $8 x + 10 y = 4$ with $\frac{1}{2} - \frac{5 y}{4}$ .

$8 (\frac{1}{2} - \frac{5 y}{4}) + 10 y = 4$

$x = \frac{1}{2} - \frac{5 y}{4}$

Simplify the left side.

Simplify $8 (\frac{1}{2} - \frac{5 y}{4}) + 10 y$ .

Simplify each term.

Apply the distributive property.

$8 (\frac{1}{2}) + 8 (- \frac{5 y}{4}) + 10 y = 4$

$x = \frac{1}{2} - \frac{5 y}{4}$

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$2 (4) (\frac{1}{2}) + 8 (- \frac{5 y}{4}) + 10 y = 4$

$x = \frac{1}{2} - \frac{5 y}{4}$

Cancel the common factor.

$2 \cdot (4 (\frac{1}{2})) + 8 (- \frac{5 y}{4}) + 10 y = 4$

$x = \frac{1}{2} - \frac{5 y}{4}$

Rewrite the expression.

$4 + 8 (- \frac{5 y}{4}) + 10 y = 4$

$x = \frac{1}{2} - \frac{5 y}{4}$

$4 + 8 (- \frac{5 y}{4}) + 10 y = 4$

$x = \frac{1}{2} - \frac{5 y}{4}$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{5 y}{4}$ into the numerator.

$4 + 8 (\frac{- 5 y}{4}) + 10 y = 4$

$x = \frac{1}{2} - \frac{5 y}{4}$

Factor $4$ out of $8$ .

$4 + 4 (2) (\frac{- 5 y}{4}) + 10 y = 4$

$x = \frac{1}{2} - \frac{5 y}{4}$

Cancel the common factor.

$4 + 4 \cdot (2 (\frac{- 5 y}{4})) + 10 y = 4$

$x = \frac{1}{2} - \frac{5 y}{4}$

Rewrite the expression.

$4 + 2 (- 5 y) + 10 y = 4$

$x = \frac{1}{2} - \frac{5 y}{4}$

$4 + 2 (- 5 y) + 10 y = 4$

$x = \frac{1}{2} - \frac{5 y}{4}$

Multiply $- 5$ by $2$ .

$4 - 10 y + 10 y = 4$

$x = \frac{1}{2} - \frac{5 y}{4}$

$4 - 10 y + 10 y = 4$

$x = \frac{1}{2} - \frac{5 y}{4}$

Combine the opposite terms in $4 - 10 y + 10 y$ .

Add $- 10 y$ and $10 y$ .

$4 + 0 = 4$

$x = \frac{1}{2} - \frac{5 y}{4}$

Add $4$ and $0$ .

$4 = 4$

$x = \frac{1}{2} - \frac{5 y}{4}$

$4 = 4$

$x = \frac{1}{2} - \frac{5 y}{4}$

$4 = 4$

$x = \frac{1}{2} - \frac{5 y}{4}$

$4 = 4$

$x = \frac{1}{2} - \frac{5 y}{4}$

$4 = 4$

$x = \frac{1}{2} - \frac{5 y}{4}$

Step 3

Remove any equations from the system that are always true.

$x = \frac{1}{2} - \frac{5 y}{4}$

Step 4

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