Question

Solve this system of linear equations. -14x + 11y = 23 7x - 3y = 37
x=? y=?

Answer 1

To solve the linear system given by -14x + 11y = 23 and 7x - 3y = 37, we used the elimination method, which resulted in finding the solution x = 13.6 and y = 19.4.

Step-by-step explanation:

To solve the system of linear equations given by -14x + 11y = 23 and 7x - 3y = 37, you can use the method of substitution or elimination. Here, I'll demonstrate the elimination method:

1. Multiply the second equation by 2 to make the coefficients of x in both equations equal in magnitude but opposite in sign:
   2(7x - 3y) = 2(37)
   14x - 6y = 74
2. Add this equation to the first equation:
   -14x + 11y + 14x - 6y = 23 + 74
   5y = 97
3. Divide by 5 to find y:
   y = 97 / 5
   y = 19.4
4. Substitute y = 19.4 into the first or second original equation to find x. Using the first equation:
   -14x + 11(19.4) = 23
   -14x + 213.4 = 23
   -14x = 23 - 213.4
   -14x = -190.4
   x = -190.4 / -14
   x = 13.6

Therefore, the solution to the system of equations is x = 13.6 and y = 19.4.

Answer 2

-14x + 11y = 23
+2(7x - 3y = 37)
----------------------
0 + 5y = 97
y = 97/5
y = 19.4

7x - 3(19.4) = 37
7x - 58.2 = 37
7x = 37 + 58.2
7x = 95.2
x = 95.2/7
x = 13.6

Check

-14(13.6) + 11(19.4) = 23
-190.4 + 213.4 = 23