Solve -2y+15y=-24,2x+9y=24 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$-2y+15y=-24,2x+9y=24$$

Solve for y, x

$x = \frac{264}{13} = 20\frac{4}{13} \approx 20.307692308$
$y = -\frac{24}{13} = -1\frac{11}{13} \approx -1.846153846$

Solution Steps

Consider the first equation. Combine $-2y$ and $15y$ to get $13y$.

$$13y=-24$$

Divide both sides by $13$.

$$y=-\frac{24}{13}$$

Consider the second equation. Insert the known values of variables into the equation.

$$2x+9\left(-\frac{24}{13}\right)=24$$

Multiply $9$ and $-\frac{24}{13}$ to get $-\frac{216}{13}$.

$$2x-\frac{216}{13}=24$$

Add $\frac{216}{13}$ to both sides.

$$2x=24+\frac{216}{13}$$

Add $24$ and $\frac{216}{13}$ to get $\frac{528}{13}$.

$$2x=\frac{528}{13}$$

Divide both sides by $2$.

$$x=\frac{\frac{528}{13}}{2}$$

Express $\frac{\frac{528}{13}}{2}$ as a single fraction.

$$x=\frac{528}{13\times 2}$$

Multiply $13$ and $2$ to get $26$.

$$x=\frac{528}{26}$$

Reduce the fraction $\frac{528}{26}$ to lowest terms by extracting and canceling out $2$.

$$x=\frac{264}{13}$$

The system is now solved.

$$y=-\frac{24}{13}$$ $$x=\frac{264}{13}$$