Question

Which statement about the pair of equations is true?

x = -2y + 300
3y = 800 - 4x

A)
The equation pair has no solutions.
Eliminate

B)
The equation pair has many solutions.


C)
The equation pair has exactly 1 solution.


D)
The equation pair has exactly 2 solutions.

Answer 1

Substitute x = -2y + 300 into 3y = 800 - 4x

3y = 8y - 400

Solve for y in 3y = 8y - 400

y = 80

Substitute y = 80 into x = -2y + 300

x = 140

Therefore,

x = 140

y = 80

Answer: D. The equation pair has exactly 2 solutions

Answer 2

C) The equation pair has exactly 1 solution.

Explanation:

Rewrite the pair of equations

x + 2y = 300

4x + 3y = 800

Multiply the first equation by 4.

4x + 8y = 1200

4x + 3y = 800

Subtract the second equation from the first: 5y = 400 → y = 80 

Putting this value back in the original equation, x = -160 + 300 = 140

The equation pair has exactly 1 solution, x = 140, y = 80