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 by the elimination method, we want to eliminate one of the variables by adding or subtracting the two equations. Let's eliminate the x-variable.

First, we'll multiply the first equation by 3 and the second equation by -1/3 to make the coefficients of the x-terms the same but opposite:

(3)(3x - 5y) = (3)(4) --> 9x - 15y = 12
(-1/3)(-9x + 3y) = (-1/3)(-24) --> 3x - y = 8

Now, we'll add the two equations together to eliminate the x-variable:

(9x - 15y) + (3x - y) = 12 + 8
12x - 16y = 20

To solve for y, divide both sides of the equation by -16:

-16y = -20
y = (-20) / (-16)
y = 5/4

Now that we have the y-value, we can substitute it back into either of the original equations to solve for x. Let's use the first equation:

3x - 5(5/4) = 4
3x - 25/4 = 4

To simplify the equation, let's multiply by 4 to get rid of the fraction:

12x - 25 = 16
12x = 16 + 25
12x = 41
x = 41 / 12

So, the solution to the system of equations is (41/12, 5/4).