Solve by Substitution 5x+6y=4 , 10x+12y=8

$5 x + 6 y = 4$ , $10 x + 12 y = 8$

Step 1

Solve for $x$ in $5 x + 6 y = 4$ .

Subtract $6 y$ from both sides of the equation.

$5 x = 4 - 6 y$

$10 x + 12 y = 8$

Divide each term in $5 x = 4 - 6 y$ by $5$ and simplify.

Divide each term in $5 x = 4 - 6 y$ by $5$ .

$\frac{5 x}{5} = \frac{4}{5} + \frac{- 6 y}{5}$

$10 x + 12 y = 8$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{4}{5} + \frac{- 6 y}{5}$

$10 x + 12 y = 8$

Divide $x$ by $1$ .

$x = \frac{4}{5} + \frac{- 6 y}{5}$

$10 x + 12 y = 8$

$x = \frac{4}{5} + \frac{- 6 y}{5}$

$10 x + 12 y = 8$

$x = \frac{4}{5} + \frac{- 6 y}{5}$

$10 x + 12 y = 8$

Simplify the right side.

Move the negative in front of the fraction.

$x = \frac{4}{5} - \frac{6 y}{5}$

$10 x + 12 y = 8$

$x = \frac{4}{5} - \frac{6 y}{5}$

$10 x + 12 y = 8$

$x = \frac{4}{5} - \frac{6 y}{5}$

$10 x + 12 y = 8$

$x = \frac{4}{5} - \frac{6 y}{5}$

$10 x + 12 y = 8$

Step 2

Replace all occurrences of $x$ with $\frac{4}{5} - \frac{6 y}{5}$ in each equation.

Replace all occurrences of $x$ in $10 x + 12 y = 8$ with $\frac{4}{5} - \frac{6 y}{5}$ .

$10 (\frac{4}{5} - \frac{6 y}{5}) + 12 y = 8$

$x = \frac{4}{5} - \frac{6 y}{5}$

Simplify the left side.

Simplify $10 (\frac{4}{5} - \frac{6 y}{5}) + 12 y$ .

Simplify each term.

Apply the distributive property.

$10 (\frac{4}{5}) + 10 (- \frac{6 y}{5}) + 12 y = 8$

$x = \frac{4}{5} - \frac{6 y}{5}$

Cancel the common factor of $5$ .

Factor $5$ out of $10$ .

$5 (2) (\frac{4}{5}) + 10 (- \frac{6 y}{5}) + 12 y = 8$

$x = \frac{4}{5} - \frac{6 y}{5}$

Cancel the common factor.

$5 \cdot (2 (\frac{4}{5})) + 10 (- \frac{6 y}{5}) + 12 y = 8$

$x = \frac{4}{5} - \frac{6 y}{5}$

Rewrite the expression.

$2 \cdot 4 + 10 (- \frac{6 y}{5}) + 12 y = 8$

$x = \frac{4}{5} - \frac{6 y}{5}$

$2 \cdot 4 + 10 (- \frac{6 y}{5}) + 12 y = 8$

$x = \frac{4}{5} - \frac{6 y}{5}$

Multiply $2$ by $4$ .

$8 + 10 (- \frac{6 y}{5}) + 12 y = 8$

$x = \frac{4}{5} - \frac{6 y}{5}$

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{6 y}{5}$ into the numerator.

$8 + 10 (\frac{- 6 y}{5}) + 12 y = 8$

$x = \frac{4}{5} - \frac{6 y}{5}$

Factor $5$ out of $10$ .

$8 + 5 (2) (\frac{- 6 y}{5}) + 12 y = 8$

$x = \frac{4}{5} - \frac{6 y}{5}$

Cancel the common factor.

$8 + 5 \cdot (2 (\frac{- 6 y}{5})) + 12 y = 8$

$x = \frac{4}{5} - \frac{6 y}{5}$

Rewrite the expression.

$8 + 2 (- 6 y) + 12 y = 8$

$x = \frac{4}{5} - \frac{6 y}{5}$

$8 + 2 (- 6 y) + 12 y = 8$

$x = \frac{4}{5} - \frac{6 y}{5}$

Multiply $- 6$ by $2$ .

$8 - 12 y + 12 y = 8$

$x = \frac{4}{5} - \frac{6 y}{5}$

$8 - 12 y + 12 y = 8$

$x = \frac{4}{5} - \frac{6 y}{5}$

Combine the opposite terms in $8 - 12 y + 12 y$ .

Add $- 12 y$ and $12 y$ .

$8 + 0 = 8$

$x = \frac{4}{5} - \frac{6 y}{5}$

Add $8$ and $0$ .

$8 = 8$

$x = \frac{4}{5} - \frac{6 y}{5}$

$8 = 8$

$x = \frac{4}{5} - \frac{6 y}{5}$

$8 = 8$

$x = \frac{4}{5} - \frac{6 y}{5}$

$8 = 8$

$x = \frac{4}{5} - \frac{6 y}{5}$

$8 = 8$

$x = \frac{4}{5} - \frac{6 y}{5}$

Step 3

Remove any equations from the system that are always true.

$x = \frac{4}{5} - \frac{6 y}{5}$

Step 4

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