What is the solution of this system?
2x + 3y = 32
11y − 2x = 52
A.
x = 3/2 , y = 5
B.
x = 4, y = 8
C.
x = 7, y = 6
D.
x = 10, y = 4
E.
x = 8, y = 16/3
You could just test each answer pair and see which works, but ...
just as quick to solve it
rewrite in the proper order
2x + 3y = 32
-2x + 11y = 52
just add them:
14y = 84
y = 6
looks like c)
let's confirem
sub y = 6 into 1st
2x +18 = 32
2x = 14
x = 7
YUP, it is c)
To find the solution of the given system of equations, we will use the method of substitution or elimination. Let's solve it using the elimination method:
1. Multiply the first equation by 11 and the second equation by 2 to make the coefficients of x in both equations equal:
Equation 1: 22x + 33y = 352
Equation 2: 22y - 4x = 104
2. Now, subtract Equation 2 from Equation 1 to eliminate x:
(22x + 33y) - (22y - 4x) = 352 - 104
Simplifying, we get:
22x + 33y - 22y + 4x = 248
Combining like terms, we have:
(22x + 4x) + (33y - 22y) = 248
26x + 11y = 248
3. Solving this new equation along with the original equation 11y - 2x = 52 by the elimination method:
Multiply the first equation by 2 and the second equation by 26 to make the coefficients of x in both equations equal:
Equation 1: 52x + 66y = 704
Equation 2: 52y - 52x = 1352
4. Now, add Equation 1 and Equation 2 to eliminate x:
(52x + 66y) + (52y - 52x) = 704 + 1352
Simplifying, we get:
52x - 52x + 66y + 52y = 2048
Combining like terms, we have:
66y + 52y = 2048
118y = 2048
Dividing both sides by 118, we have:
y = 2048/118
y ≈ 17.355
5. Substitute the value of y in either of the original equations to find the value of x. Let's substitute it in Equation 1:
2x + 3(17.355) = 32
2x + 52.065 = 32
Subtracting 52.065 from both sides, we get:
2x = 32 - 52.065
2x = -20.065
Dividing both sides by 2, we have:
x = -20.065/2
x ≈ -10.033
Therefore, the solution to the given system of equations is approximately x = -10.033 and y ≈ 17.355.
None of the provided answer options matches the solution we found, so none of the given options is correct.