Solve the following system of equations using the elimination method.

Question

3x−4y=−4 , x+3y=−10

(1 point)
Responses

(−4,−2)
left parenthesis negative 4 comma negative 2 right parenthesis

(−16,2)
left parenthesis negative 16 comma 2 right parenthesis

(−16,−2)
left parenthesis negative 16 comma negative 2 right parenthesis

(−2,−4)
left parenthesis negative 2 comma negative 4 right parenthesis

Answer 1

To solve the system of equations using the elimination method, we can multiply the second equation by 4 to get the coefficients of y to be the same:

4(x+3y) = 4(-10)
4x + 12y = -40

Now, we can subtract the first equation from the second equation:

(4x + 12y) - (3x - 4y) = -40 - (-4)
4x + 12y - 3x + 4y = -40 + 4
x + 16y = -36

Now we have a new equation:

x + 16y = -36

We can solve this equation for x:

x = -36 - 16y

Now we can substitute this expression for x into either of the original equations. Let's use the first equation:

3x - 4y = -4
3(-36 - 16y) - 4y = -4
-108 - 48y - 4y = -4
-108 - 52y = -4
-52y = -4 + 108
-52y = 104
y = 104/-52
y = -2

Substituting the value of y back into the expression for x:

x = -36 - 16(-2)
x = -36 + 32
x = -4

Therefore, the solution to the system of equations is (-4, -2).