Question

2x - 3y = 9 -5x – 3y = 30 Elimination method

Answer 1

Answer:

The solution to the system of the equations be:

• (x, y) = (-3, -5)

Step-by-step explanation:

Given the system of equations

$2x - 3y = 9$

$-5x - 3y = 30$

Solving the system of equations using the elimination method

Multiply $2x-3y=9$ by 5:  $10x-15y=45$

Multiply $-5x-3y=30$ by 2:  $-10x-6y=60$

$\begin{bmatrix}10x-15y=45\\ -10x-6y=60\end{bmatrix}$

adding the equations

$-10x-6y=60$

$+$

$\underline{10x-15y=45}$

$-21y=105$

now solving -21y = 105 for y

$-21y=105$

Divide both sides by -21

$\frac{-21y}{-21}=\frac{105}{-21}$

Simplify

$y=-5$

For 10x - 15y = 45 plug in y = -5

$10x-15\left(-5\right)=45$

Apply the rule -a(-a) = a

$10x+15\cdot \:5=45$

$10x+75=45$

Subtract 75 from both sides

$10x+75-75=45-75$

Simplify

$10x=-30$

Divide both sides by 10

$\frac{10x}{10}=\frac{-30}{10}$

Simplify

$x=-3$

Therefore, the solution to the system of the equations be:

• (x, y) = (-3, -5)

The graph of the solution to the system of equations is also attached below.