Question

X=-2y+16
4x+8y=32
substitutional equation

Answer 1

To solve the given system of equations x = -2y + 16 and x + 8y = 32, substitute the value of x into the second equation and solve for y. Then, substitute the value of y into the first equation and solve for x. The solution is x = 32/3 and y = 8/3.

Step-by-step explanation:

To solve the given system of equations:

x = -2y + 16

x + 8y = 32

1. Since we have x = -2y + 16, we can substitute this value for x in the second equation:
2. (-2y + 16) + 8y = 32
3. Simplifying the equation, we get:
4. 6y + 16 = 32
5. Subtracting 16 from both sides, we have:
6. 6y = 16
7. Dividing both sides by 6, we get:
8. y = 16/6
9. Simplifying the fraction, we have:
10. y = 8/3
11. To find the corresponding value of x, we substitute y = 8/3 into the first equation:
12. x = -2(8/3) + 16
13. Simplifying, we get:
14. x = -16/3 + 16
15. Combining fractions, we have:
16. x = (16 - 16/3)/3
17. Common denominator is 3, so we have:
18. x = (48/3 - 16/3)/3
19. Subtracting fractions, we get:
20. x = 32/3

Therefore, the solution to the system of equations is x = 32/3 and y = 8/3.