Question

What is the solution to the system of equations below?

y = -1/3x + 9 and y = 2/3x - 12.
Options:
a) (21, 2)
b) (21, -10)
c) (-21, 16)
d) (-21, -26)

Answer 1

By setting the given linear equations equal and solving for x, and then substituting the value of x into one of the equations to solve for y, we find that the solution to the system of equations is (21, 2), matching option a.

Step-by-step explanation:

The student asked for the solution to the system of linear equations given by y = -1/3x + 9 and y = 2/3x - 12. To find the solution, set the two equations equal to each other and solve for x:

• -1/3x + 9 = 2/3x - 12
• Add 1/3x to both sides: 9 = x - 12
• Add 12 to both sides: x = 21

Now, substitute x = 21 into either equation to solve for y:

• y = 2/3(21) - 12
• y = 14 - 12
• y = 2

Therefore, the solution to the system of equations is the coordinate (21, 2), which corresponds to option a.