Solve by Substitution 4x+5y=3 , 8x+10y=6

$4 x + 5 y = 3$ , $8 x + 10 y = 6$

Step 1

Solve for $x$ in $4 x + 5 y = 3$ .

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

$4 x = 3 - 5 y$

$8 x + 10 y = 6$

Divide each term in $4 x = 3 - 5 y$ by $4$ and simplify.

Divide each term in $4 x = 3 - 5 y$ by $4$ .

$\frac{4 x}{4} = \frac{3}{4} + \frac{- 5 y}{4}$

$8 x + 10 y = 6$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{3}{4} + \frac{- 5 y}{4}$

$8 x + 10 y = 6$

Divide $x$ by $1$ .

$x = \frac{3}{4} + \frac{- 5 y}{4}$

$8 x + 10 y = 6$

$x = \frac{3}{4} + \frac{- 5 y}{4}$

$8 x + 10 y = 6$

$x = \frac{3}{4} + \frac{- 5 y}{4}$

$8 x + 10 y = 6$

Simplify the right side.

Move the negative in front of the fraction.

$x = \frac{3}{4} - \frac{5 y}{4}$

$8 x + 10 y = 6$

$x = \frac{3}{4} - \frac{5 y}{4}$

$8 x + 10 y = 6$

$x = \frac{3}{4} - \frac{5 y}{4}$

$8 x + 10 y = 6$

$x = \frac{3}{4} - \frac{5 y}{4}$

$8 x + 10 y = 6$

Step 2

Replace all occurrences of $x$ with $\frac{3}{4} - \frac{5 y}{4}$ in each equation.

Replace all occurrences of $x$ in $8 x + 10 y = 6$ with $\frac{3}{4} - \frac{5 y}{4}$ .

$8 (\frac{3}{4} - \frac{5 y}{4}) + 10 y = 6$

$x = \frac{3}{4} - \frac{5 y}{4}$

Simplify the left side.

Simplify $8 (\frac{3}{4} - \frac{5 y}{4}) + 10 y$ .

Simplify each term.

Apply the distributive property.

$8 (\frac{3}{4}) + 8 (- \frac{5 y}{4}) + 10 y = 6$

$x = \frac{3}{4} - \frac{5 y}{4}$

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$4 (2) (\frac{3}{4}) + 8 (- \frac{5 y}{4}) + 10 y = 6$

$x = \frac{3}{4} - \frac{5 y}{4}$

Cancel the common factor.

$4 \cdot (2 (\frac{3}{4})) + 8 (- \frac{5 y}{4}) + 10 y = 6$

$x = \frac{3}{4} - \frac{5 y}{4}$

Rewrite the expression.

$2 \cdot 3 + 8 (- \frac{5 y}{4}) + 10 y = 6$

$x = \frac{3}{4} - \frac{5 y}{4}$

$2 \cdot 3 + 8 (- \frac{5 y}{4}) + 10 y = 6$

$x = \frac{3}{4} - \frac{5 y}{4}$

Multiply $2$ by $3$ .

$6 + 8 (- \frac{5 y}{4}) + 10 y = 6$

$x = \frac{3}{4} - \frac{5 y}{4}$

Cancel the common factor of $4$ .

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

$6 + 8 (\frac{- 5 y}{4}) + 10 y = 6$

$x = \frac{3}{4} - \frac{5 y}{4}$

Factor $4$ out of $8$ .

$6 + 4 (2) (\frac{- 5 y}{4}) + 10 y = 6$

$x = \frac{3}{4} - \frac{5 y}{4}$

Cancel the common factor.

$6 + 4 \cdot (2 (\frac{- 5 y}{4})) + 10 y = 6$

$x = \frac{3}{4} - \frac{5 y}{4}$

Rewrite the expression.

$6 + 2 (- 5 y) + 10 y = 6$

$x = \frac{3}{4} - \frac{5 y}{4}$

$6 + 2 (- 5 y) + 10 y = 6$

$x = \frac{3}{4} - \frac{5 y}{4}$

Multiply $- 5$ by $2$ .

$6 - 10 y + 10 y = 6$

$x = \frac{3}{4} - \frac{5 y}{4}$

$6 - 10 y + 10 y = 6$

$x = \frac{3}{4} - \frac{5 y}{4}$

Combine the opposite terms in $6 - 10 y + 10 y$ .

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

$6 + 0 = 6$

$x = \frac{3}{4} - \frac{5 y}{4}$

Add $6$ and $0$ .

$6 = 6$

$x = \frac{3}{4} - \frac{5 y}{4}$

$6 = 6$

$x = \frac{3}{4} - \frac{5 y}{4}$

$6 = 6$

$x = \frac{3}{4} - \frac{5 y}{4}$

$6 = 6$

$x = \frac{3}{4} - \frac{5 y}{4}$

$6 = 6$

$x = \frac{3}{4} - \frac{5 y}{4}$

Step 3

Remove any equations from the system that are always true.

$x = \frac{3}{4} - \frac{5 y}{4}$

Step 4

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