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
To use the elimination method, we need to manipulate one or both of the equations so that when added or subtracted, one of the variables will be eliminated.
Starting with the given system of equations:
1) 9x - 7y = 22
2) x + 3y = -24
Let's multiply equation 2 by 9 to create a common coefficient for x:
1) 9x - 7y = 22
2) 9x + 27y = -216
Now, let's add the two equations together to eliminate x:
(9x - 7y) + (9x + 27y) = 22 - 216
18x + 20y = -194
Now we have a new equation with just one variable. Solve for x:
18x + 20y = -194
18x = -194 - 20y
18x = -194 - 20y
x = (-194 - 20y) / 18
x = -10.7778 - 1.1111y
Now, substitute this expression for x back into equation 2:
-10.7778 - 1.1111y + 3y = -24
-7.7778 + 1.8889y = -24
1.8889y = -16.2222
y = -8.57
Now we have found the value of y, substitute back into equation 2 to find x:
x + 3(-8.57) = -24
x - 25.71 = -24
x = 1.71
Therefore, the solution to the system of equations is (1.71, -8.57).