Solve by Substitution 6y=-5x+24 2.5x+3y=12

$6 y = - 5 x + 24$ $2.5 x + 3 y = 12$

Divide each term in $6 y = - 5 x + 24$ by $6$ and simplify.

Divide each term in $6 y = - 5 x + 24$ by $6$ .

$\frac{6 y}{6} = \frac{- 5 x}{6} + \frac{24}{6}$

$2.5 x + 3 y = 12$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 y}{6} = \frac{- 5 x}{6} + \frac{24}{6}$

$2.5 x + 3 y = 12$

Divide $y$ by $1$ .

$y = \frac{- 5 x}{6} + \frac{24}{6}$

$2.5 x + 3 y = 12$

$y = \frac{- 5 x}{6} + \frac{24}{6}$

$2.5 x + 3 y = 12$

$y = \frac{- 5 x}{6} + \frac{24}{6}$

$2.5 x + 3 y = 12$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{(5) x}{6} + \frac{24}{6}$

$2.5 x + 3 y = 12$

Divide $24$ by $6$ .

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

$2.5 x + 3 y = 12$

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

$2.5 x + 3 y = 12$

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

$2.5 x + 3 y = 12$

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

$2.5 x + 3 y = 12$

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

Replace all occurrences of $y$ in $2.5 x + 3 y = 12$ with $- \frac{5 x}{6} + 4$ .

$2.5 x + 3 (- \frac{5 x}{6} + 4) = 12$

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

Simplify the left side.

Simplify $2.5 x + 3 (- \frac{5 x}{6} + 4)$ .

Simplify each term.

Apply the distributive property.

$2.5 x + 3 (- \frac{5 x}{6}) + 3 \cdot 4 = 12$

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

Cancel the common factor of $3$ .

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

$2.5 x + 3 (\frac{- 5 x}{6}) + 3 \cdot 4 = 12$

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

Factor $3$ out of $6$ .

$2.5 x + 3 (\frac{- 5 x}{3 (2)}) + 3 \cdot 4 = 12$

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

Cancel the common factor.

$2.5 x + 3 (\frac{- 5 x}{3 \cdot 2}) + 3 \cdot 4 = 12$

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

Rewrite the expression.

$2.5 x + \frac{- 5 x}{2} + 3 \cdot 4 = 12$

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

$2.5 x + \frac{- 5 x}{2} + 3 \cdot 4 = 12$

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

Multiply $3$ by $4$ .

$2.5 x + \frac{- 5 x}{2} + 12 = 12$

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

Move the negative in front of the fraction.

$2.5 x - \frac{5 x}{2} + 12 = 12$

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

$2.5 x - \frac{5 x}{2} + 12 = 12$

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

To write $2.5 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$2.5 x \cdot \frac{2}{2} - \frac{5 x}{2} + 12 = 12$

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

Simplify terms.

Combine $2.5 x$ and $\frac{2}{2}$ .

$\frac{2.5 x \cdot 2}{2} - \frac{5 x}{2} + 12 = 12$

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

Combine the numerators over the common denominator.

$\frac{2.5 x \cdot 2 - 5 x}{2} + 12 = 12$

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

$\frac{2.5 x \cdot 2 - 5 x}{2} + 12 = 12$

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

Simplify each term.

Simplify the numerator.

Factor $2.5 x$ out of $2.5 x \cdot 2 - 5 x$ .

Move $x$ .

$\frac{2.5 \cdot (2 x) - 5 x}{2} + 12 = 12$

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

Factor $2.5 x$ out of $2.5 \cdot 2 x$ .

$\frac{2.5 x (2) - 5 x}{2} + 12 = 12$

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

Factor $2.5 x$ out of $- 5 x$ .

$\frac{2.5 x (2) + 2.5 x (- 2)}{2} + 12 = 12$

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

Factor $2.5 x$ out of $2.5 x (2) + 2.5 x (- 2)$ .

$\frac{2.5 x (2 - 2)}{2} + 12 = 12$

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

$\frac{2.5 x (2 - 2)}{2} + 12 = 12$

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

Combine exponents.

Multiply $2 - 2$ by $2.5$ .

$\frac{0 x}{2} + 12 = 12$

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

Multiply $0$ by $x$ .

$\frac{0}{2} + 12 = 12$

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

$\frac{0}{2} + 12 = 12$

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

$\frac{0}{2} + 12 = 12$

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

Divide $0$ by $2$ .

$0 + 12 = 12$

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

$0 + 12 = 12$

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

Add $0$ and $12$ .

$12 = 12$

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

$12 = 12$

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

$12 = 12$

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

$12 = 12$

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

Remove any equations from the system that are always true.

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

Solve by Substitution 6y=-5x+24 2.5x+3y=12

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