Question

Which set of coordinates satisfies the equations 3x - 2y = 15 and 4x - y = 20?

1) (2,-7)
2) (1,-6)
3) (5,0)
4) (0,-7.5)

Answer 1

The set of coordinates that satisfy the equations 3x - 2y = 15 and 4x - y = 20 is (5, 0).

Step-by-step explanation:

The set of coordinates that satisfies the equations 3x - 2y = 15 and 4x - y = 20 can be found by solving the system of equations. Here are the steps:

1. Start with the first equation: 3x - 2y = 15
2. Isolate x by adding 2y to both sides: 3x = 2y + 15
3. Divide both sides by 3: x = (2y + 15) / 3
4. Substitute this value of x into the second equation: 4((2y + 15) / 3) - y = 20
5. Simplify the equation: (8y + 60) / 3 - y = 20
6. Multiply both sides by 3 to eliminate the fraction: 8y + 60 - 3y = 60
7. Combine like terms: 5y + 60 = 60
8. Subtract 60 from both sides: 5y = 0
9. Divide both sides by 5: y = 0
10. Substitute y = 0 back into the first equation to find x: 3x - 2(0) = 15
11. Simplify: 3x = 15
12. Divide both sides by 3: x = 5

The set of coordinates that satisfies both equations is (5, 0), which corresponds to answer choice 3.