If 7x + 4y = 18 and 3x + y = -3, what is the value of x + y?
F. 9
G. 11
H. 12
J. 14
K. 15
7x + 4y = 18
3x + y = -3
y = -3 -3x
7x + 4(-3 -3x) = 18
7x - 12 - 12x = 18
-5x = 18 + 12
-5x = 30
x = -6
3(-6) + y = -3
y = 18 - 3
y = 15
15 + (-6) = ?
15 - 6 = 9
Yes.
Thank you so much, Ms. Sue.
You're very welcome.
To find the value of x + y, you need to solve the system of equations given. Here's how to do it:
Step 1: Start by solving one of the equations for one variable in terms of the other variable.
Let's solve the second equation, 3x + y = -3, for y:
y = -3 - 3x
Step 2: Substitute this expression for y into the first equation, 7x + 4y = 18.
7x + 4(-3 - 3x) = 18
Simplify the equation:
7x - 12 - 12x = 18
Combine like terms:
-5x - 12 = 18
Step 3: Solve for x. Add 12 to both sides of the equation to isolate the term with x.
-5x = 18 + 12
-5x = 30
Now divide both sides by -5 to solve for x:
x = -30 / -5
x = 6
Step 4: Substitute the value of x into one of the original equations to solve for y.
Let's use the second equation, 3x + y = -3.
3(6) + y = -3
18 + y = -3
Subtract 18 from both sides of the equation to isolate the term with y.
y = -3 - 18
y = -21
Step 5: Now that we know the values of x and y, we can find x + y.
x + y = 6 + (-21)
x + y = -15
Therefore, the value of x + y is -15.
So, the correct answer is not listed among the options given.