Question Use the elimination method to solve the follow system of equations. 9x−7y=22 x+3y=−24 This question requires you to show your work. (1 point)
Responses
(3,−9)
(4, 2)
(0,−8)
(−3,−7)
show your work. no matrix system choose one of the answers listed.
To solve this system of equations using the elimination method, we can first multiply the second equation by 7 to make the coefficients of y the same in both equations:
7(x + 3y) = 7*(-24)
7x + 21y = -168
Now we have the system of equations:
9x − 7y = 22
7x + 21y = -168
Next, we can add the two equations together to eliminate y:
9x − 7y + 7x + 21y = 22 - 168
16x + 14y = -146
Divide by 2 to simplify:
8x + 7y = -73
Now, we can add this new equation to the second original equation to eliminate y:
8x + 7y + x + 3y = -73 - 24
9x + 10y = -97
Now, we can solve this equation for x:
9x + 10y = -97
9x = -97 - 10y
x = (-97 - 10y)/9
Next, substitute this expression for x back into the second original equation:
(-97 - 10y)/9 + 3y = -24
-97 - 10y + 27y = -216
-97 + 17y = -216
17y = -119
y = -119/17
y = -7
Now that we have found the value of y, we can substitute it back into one of the original equations to find the value of x:
x + 3*(-7) = -24
x - 21 = -24
x = -24 + 21
x = -3
Therefore, the solution to the system of equations is (x, y) = (-3, -7). This matches with the answer listed as (-3, -7).