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# Solve the following system of equations.x-9y=-135x+3y=-15

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asked 2021-04-25

Solve the following system of equations.
$$x-9y=-13$$
$$5x+3y=-15$$

## Answers (1)

2021-04-27

Step 1
The equations are given by,
$$x-9y=-13$$...(1)
$$5x+3y=-15$$...(2)
Step 2
Multiply the equation (1) by 5 and subtract with equation (2) as follows.
$$5x-45y=-65$$
$$5x+3y=-15$$
$$-48y=-50$$
$$\displaystyle{y}={\frac{{{50}}}{{{48}}}}$$
$$\displaystyle{y}={\frac{{{25}}}{{{24}}}}$$
Substitute $$\displaystyle{y}={\frac{{{25}}}{{{24}}}}$$ in equation (1).
$$\displaystyle{x}-{9}{\left({\frac{{{25}}}{{{24}}}}\right)}=-{13}$$
$$\displaystyle{x}-{\frac{{{225}}}{{{24}}}}=-{13}$$
$$\displaystyle{x}=-{13}+{\frac{{{225}}}{{{24}}}}$$
$$\displaystyle{x}=-{\frac{{{87}}}{{{24}}}}$$
$$\displaystyle{x}=-{\frac{{{29}}}{{{8}}}}$$
The solution of the system f equations are $$\displaystyle{x}=-{\frac{{{29}}}{{{8}}}},{y}={\frac{{{25}}}{{{24}}}}$$.

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