Question

Solve the system by the elimination method.

3x−5y=4

−9x+3y=−24
(1 point)
Responses

(3,1)
open paren 3 comma 1 close paren

(8,4)
open paren 8 comma 4 close paren

(2, −2)
(2, −2)

(1, −1)

Answer 1

To solve the system of equations by the elimination method, we need to eliminate one of the variables by adding or subtracting the equations. In this case, we can eliminate the variable x by multiplying the first equation by 3 and the second equation by 1, then adding the two equations together.

Multiplying the first equation by 3, we get:

(3)(3x-5y) = (3)(4)
9x - 15y = 12

Multiplying the second equation by 1, we get:

(1)(-9x+3y) = (1)(-24)
-9x + 3y = -24

Adding the two equations together, we get:

(9x - 15y) + (-9x + 3y) = 12 + (-24)
9x - 15y - 9x + 3y = -12
-12y = -12

Dividing both sides of the equation by -12, we get:

y = (-12)/(-12)
y = 1

Substituting the value of y back into one of the original equations, we can solve for x. Let's use the first equation:

3x - 5(1) = 4
3x - 5 = 4
3x = 4 + 5
3x = 9
x = 9/3
x = 3

Therefore, the solution to the system of equations is (3, 1).