Question

Solve the following system of equations using the elimination method.

3x−4y=−4 , x+3y=−10

(1 point)
Responses

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

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

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

(−16,2)

Answer 1

To solve the system of equations using the elimination method, we want to eliminate one of the variables by adding the two equations together.

Given equations:
1) 3x - 4y = -4
2) x + 3y = -10

To eliminate y, we will multiply equation 2 by 4 and equation 1 by 3, so the coefficients of y will be the same but with opposite signs. This gives us:
1) 12x - 16y = -16
2) 4x + 12y = -40

Now, we can add these two equations together to eliminate y:
(12x - 16y) + (4x + 12y) = -16 + (-40)
16x - 4y = -56

Dividing the entire equation by 4 to simplify:
4x - y = -14

Now we have a simpler equation in terms of x and y. Let's solve this equation along with equation 2:

1) x + 3y = -10 (Equation 2)
2) 4x - y = -14 (New equation)

Multiply equation 1 by 4 and equation 2 by 1 to get:
1) 4x + 12y = -40
2) 4x - y = -14

Adding these two equations together:
(4x + 12y) + (4x - y) = -40 + (-14)
8x + 11y = -54

Now, we have two equations:
1) 4x + 12y = -40
2) 8x + 11y = -54

Solving this system of equations using the elimination method, we get: x = -2 and y = -4

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