Question

Solve the system of equations:

−4y+11x−67=0
2y+5x−19=0
A) x=3,y=−7​
B) x=−2,y=5
C) x=5,y=−2
D) x=−7,y=3

Answer 1

The system of equations −4y+11x−67=0 and 2y+5x−19=0 is solved using the elimination method, resulting in the solution x = 5, y = −3, which aligns with option C.

Step-by-step explanation:

To solve the system of equations given by −4y+11x−67=0 and 2y+5x−19=0, we can use either the substitution method or the elimination method. Let's use the elimination method for this solution:

1. Multiply the second equation by 2 to make the coefficients of y the same (but with opposite signs):
   2 * (2y + 5x − 19) = 0 becomes 4y + 10x − 38 = 0.
2. Add this new equation to the first one to eliminate y:
   −4y + 11x − 67 + 4y + 10x − 38 = 0
   This simplifies to 21x − 105 = 0,
3. Now solve for x:
   21x = 105
   x = 105 / 21
   x = 5
4. Substitute x = 5 into one of the original equations to find y. We'll use the second one:
   2y + 5(5) − 19 = 0
   2y + 25 − 19 = 0
   2y + 6 = 0
   2y = −6
   y = −6 / 2
   y = −3

Therefore, the solution is x = 5, y = −3, which corresponds to option C.