Question

Solve the following system of equations using the elimination method. 3x−4y=−4 , x+3y=−10 (1 point) Responses (−16,−2) left parenthesis negative 16 comma negative 2 right parenthesis (−2,−4) left parenthesis negative 2 comma negative 4 right parenthesis (−16,2) left parenthesis negative 16 comma 2 right parenthesis (−4,−2)

Answer 1

To solve the system of equations using the elimination method, we can add the two equations together to eliminate the variable "x":

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

Simplifying this equation gives:

4x - y = -14

Now, we have a new equation with only one variable, so we can solve for "y":

4x - y = -14
y = 4x + 14

Next, substitute this expression for "y" into one of the original equations:

x + 3(4x + 14) = -10

Distribute the 3:

x + 12x + 42 = -10

Combine like terms:

13x + 42 = -10

Subtract 42 from both sides:

13x = -52

Divide by 13:

x = -4

Now that we have the value of "x", substitute it back into one of the original equations to solve for "y":

3(-4) - 4y = -4

-12 - 4y = -4

Add 12 to both sides:

-4y = 8

Divide by -4:

y = -2

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