Question

.

What is the solution to this system of equations?



2x + y = 40

x − 2y = −20

Answer 1

The solution to the system of linear equations is found using the elimination method, resulting in the solution (x, y) = (12, 16).

Step-by-step explanation:

The solution to the system of equations:

• 2x + y = 40
• x - 2y = -20

can be found using the method of substitution or elimination. For example, using the elimination method:

1. Multiply the second equation by 2 to align terms with the first equation:
   2(x - 2y) = 2(-20)
   2x - 4y = -40
2. Add this result to the first equation to eliminate x:
   2x + y + 2x - 4y = 40 - 40
   4x - 3y = 0
3. Solve for y:
   3y = 4x
   y = 4/3x
4. Substitute y = 4/3x back into the first equation:
   2x + 4/3x = 40
   10/3x = 40
   x = 12
5. Substitute x = 12 into y = 4/3x:
   y = 4/3(12)
   y = 16

The solution to the system is (x, y) = (12, 16).