Question

Given the system of equations, what is the value of x + y? x + 2y = 24 2x + y = 9

Answer 1

The value of x + y is 11.

Step-by-step explanation:

To find the value of x + y in the given system of equations:

x + 2y = 24 (Equation 1)

2x + y = 9 (Equation 2)

1. Start by solving Equation 1 for x:

• Subtract 2y from both sides: x = 24 - 2y

Substitute this value of x into Equation 2:

• 2(24 - 2y) + y = 9
• 48 - 4y + y = 9
• Combine like terms: -3y = -39
• Divide both sides by -3: y = 13

Substitute this value of y back into Equation 1:

• x + 2(13) = 24
• x + 26 = 24
• Subtract 26 from both sides: x = -2

Finally, find the value of x + y:

• -2 + 13 = 11

Answer 2

11

Step-by-step explanation:

x + 2y = 24.....x = 24 - 2y

now sub 24 - 2y in for x, back into the other equation

2x + y = 9

2(24 -2y) + y = 9

48 - 4y + y = 9

-4y + y = 9 - 48

-3y = - 39

y = -39/-3

y = 13

x + 2y = 24

x + 2(13) = 24

x + 26 = 24

x = 24 - 26

x = -2

so the value of x + y = -2 + 13 = 11 <===