Answer:
x = 2
y = -13/5
Explanation:
Let's solve this system of equations step by step:
1. We are given that z = 5. We can substitute this value into the second equation:
4x - 5y + 3z = 36
4x - 5y + 3(5) = 36
4x - 5y + 15 = 36
2. Now, let's simplify the second equation:
4x - 5y + 15 = 36
4x - 5y = 36 - 15
4x - 5y = 21
3. We have two equations now:
2x + 5y + 2 = -7
4x - 5y = 21
4. Let's eliminate one variable, either x or y. We'll eliminate y by adding the two equations:
(2x + 5y + 2) + (4x - 5y) = (-7) + 21
2x + 4x + 2 = 14
6x + 2 = 14
5. Now, subtract 2 from both sides to isolate 6x:
6x = 14 - 2
6x = 12
6. Divide both sides by 6 to solve for x:
x = 12 / 6
x = 2
7. Now that we have the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the first equation:
2x + 5y + 2 = -7
2(2) + 5y + 2 = -7
4 + 5y + 2 = -7
8. Simplify:
5y + 6 = -7
9. Subtract 6 from both sides:
5y = -7 - 6
5y = -13
10. Finally, divide by 5 to solve for y:
y = -13 / 5
So, the solution to the system of equations when z = 5 is:
x = 2
y = -13/5