Question

Solve for x and y in the system of equations:

-2x + y = 4
7x - 2y = 7
a) x = 3, y = 10
b) x = 2, y = 5
c) x = 1, y = 2
d) x = -3, y = 10

Answer 1

The system of equations -2x + y = 4 and 7x - 2y = 7 is solved using the elimination method to find that x = 5 and y = 14, which is not among the multiple-choice answers provided.

The correct option is not given.

Step-by-step explanation:

To solve the system of equations -2x + y = 4 and 7x - 2y = 7, we can use the substitution or elimination method. For this solution, I will use the elimination method:

1. Multiply the first equation by 2 so that the coefficients of y have the same absolute value but opposite signs. This gives us -4x + 2y = 8.
2. The new system of equations is now:

• -4x + 2y = 8
• 7x - 2y = 7

1. Add the two equations to eliminate y: 3x = 15.
2. Divide by 3 to solve for x: x = 5.
3. Substitute x back into the first original equation to solve for y: -2(5) + y = 4 which simplifies to y = 14.

Therefore, the solution is x = 5 and y = 14.

Note that this solution is not among the options provided by the student, so the correct answer must be written separately, and none of the provided multiple-choice answers (a, b, c, or d) are correct.

The correct option is not given.