Systems of Linear Equations Unit Test

Question

10 of 1410 of 14 Items

Question
Solve the system of equations.
−6x+2y=−32

4x+3y=−9
(1 point)
(
,
)

Answer 1

To solve the system of equations:

1. $-6x+2y=-32$
2. $4x+3y=-9$

We can use either the substitution method or the elimination method. Here, we'll use the elimination method.

First, we can simplify the first equation. Divide the entire equation by 2:

$$-3x+y=-16$$

Now we can rewrite the system of equations:

1. $-3x+y=-16$
2. $4x+3y=-9$

Next, we can express $y$ from the first equation:

$$y=3x-16$$

Now, substitute $y$ in the second equation:

$$4x+3(3x-16)=-9$$

Distributing:

$$4x+9x-48=-9$$

Combine like terms:

$$13x-48=-9$$

Add 48 to both sides:

$$13x=39$$

Divide by 13:

$$x=3$$

Now, substitute $x=3$ back into the equation for $y$:

$$y=3(3)-16$$ $$y=9-16$$ $$y=-7$$

So, the solution to the system of equations is:

$$\boxed{{\displaystyle (3,-7)}}$$