Question

Solve the system of equations:

5x + 7y = 97
x + y = 15

A) x = 11, y = 4
B) x = 10, y = 5
C) x = 9, y = 6
D) x = 8, y = 7

Answer 1

To solve the system of equations 5x + 7y = 97 and x + y = 15, isolate one variable in one of the equations, substitute the value back into the equation, and solve for the variable. The correct answer is option A) x = 4, y = 11.

Step-by-step explanation:

To solve the system of equations:

5x + 7y = 97

x + y = 15

1. Begin by isolating one variable in one of the equations. Let's isolate x in the second equation.
2. x = 15 - y
3. Substitute this value of x into the first equation.
4. 5(15 - y) + 7y = 97
5. Distribute and simplify.
6. 75 - 5y + 7y = 97
7. 75 + 2y = 97
8. Combine like terms.
9. 2y = 22
10. Divide both sides by 2 to solve for y.
11. y = 11
12. Substitute this value of y back into the second equation to solve for x.
13. x + 11 = 15
14. x = 15 - 11
15. x = 4
16. The solution to the system of equations is x = 4 and y = 11. Therefore, the correct answer is option A) x = 4, y = 11.