Question

Solve the following system of equations using the elimination method. 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)

Answer 1

To solve the system of equations using the elimination method, we will eliminate one of the variables by adding or subtracting the two equations.

Let's eliminate the variable x.

First, we will multiply the second equation by 3 to make the x coefficients in both equations equal.

3(x + 3y) = 3(-10)
3x + 9y = -30

Now, we can write the revised system of equations:

3x - 4y = -4
3x + 9y = -30

Subtract the first equation from the second equation:

(3x + 9y) - (3x - 4y) = (-30) - (-4)
3x + 9y - 3x + 4y = -30 + 4
13y = -26
y = -26/13
y = -2

Substitute the value of y into the first equation:

3x - 4(-2) = -4
3x + 8 = -4
3x = -12
x = -12/3
x = -4

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