Solve 172p + 15y = 50; 15x + 17y = 49 | Equatix - Math Solver

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Example

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

a⋅(b-2)=3b

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

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Question

$$172p+15y=50; 15x+17y=49$$

Solve for x, y

$x=\frac{2924p}{225}-\frac{23}{45}$
$y=-\frac{172p}{15}+\frac{10}{3}$

Steps Using Substitution

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

$$15y+172p=50,17y+15x=49$$

Pick one of the two equations which is more simple to solve for $y$ by isolating $y$ on the left hand side of the equal sign.

$$15y+172p=50$$

Subtract $172p$ from both sides of the equation.

$$15y=50-172p$$

Divide both sides by $15$.

$$y=-\frac{172p}{15}+\frac{10}{3}$$

Substitute $\frac{10}{3}-\frac{172p}{15}$ for $y$ in the other equation, $17y+15x=49$.

$$17\left(-\frac{172p}{15}+\frac{10}{3}\right)+15x=49$$

Multiply $17$ times $\frac{10}{3}-\frac{172p}{15}$.

$$-\frac{2924p}{15}+\frac{170}{3}+15x=49$$

Subtract $\frac{170}{3}-\frac{2924p}{15}$ from both sides of the equation.

$$15x=\frac{2924p}{15}-\frac{23}{3}$$

Divide both sides by $15$.

$$x=\frac{2924p}{225}-\frac{23}{45}$$

The system is now solved.

$$y=-\frac{172p}{15}+\frac{10}{3},x=\frac{2924p}{225}-\frac{23}{45}$$