Question

Solve the system of linear equations:
2x + y = -5
2x + 3y = 10

Answer 1

The solution to the given system of linear equations is x = -25/4 and y = 7.5.

Step-by-step explanation:

To solve the system of linear equations:

2x + y = -5

2x + 3y = 10

We can use the method of substitution:

1. Choose one of the equations and solve for one variable in terms of the other. Let's solve the first equation for y:
2. y = -5 - 2x
3. Substitute this value of y into the other equation:
4. 2x + 3(-5 - 2x) = 10
5. Distribute and simplify:
6. 2x - 15 - 6x = 10
7. -4x - 15 = 10
8. Add 15 to both sides:
9. -4x = 25
10. Divide by -4:
11. x = -rac{25}{4}
12. Substitute this value of x back into one of the original equations to solve for y. Let's use the first equation:
13. 2(-rac{25}{4}) + y = -5
14. -rac{25}{2} + y = -5
15. Add rac{25}{2} to both sides:
16. y = -5 + rac{25}{2}
17. y = -5 + 12.5
18. y = 7.5

Therefore, the solution to the system of linear equations is x = -rac{25}{4} and y = 7.5.