Final answer:
The solution to the system of linear equations 4x + 3y = 25 and 5x + 2y = 33 is found using the elimination method. The solution is (x, y) = (7, -1), which was checked by substituting back into the original equations.
Step-by-step explanation:
To solve the system of equations algebraically, we will use the method of substitution or elimination. Let's solve the given system:
- 4x + 3y = 25
- 5x + 2y = 33
We could start with either of these methods, but elimination looks convenient here. We'll multiply the first equation by 2 and the second by 3 to align the y terms:
- 8x + 6y = 50
- 15x + 6y = 99
Now subtract the first new equation from the second one:
- 15x - 8x + 6y - 6y = 99 - 50
- 7x = 49
- x = 7
Substitute x = 7 back into one of the original equations to find y:
- 4x + 3y = 25
- 4(7) + 3y = 25
- 3y = 25 - 28
- 3y = -3
- y = -1
We find that x = 7 and y = -1. To check, we substitute these values back into both original equations:
- 4(7) + 3(-1) should equal 25
- 28 - 3 = 25 ✓
- 5(7) + 2(-1) should equal 33
- 35 - 2 = 33 ✓
Both checks are correct, so the solution to the system is (x, y) = (7, -1).