Question

On a coordinate plane, 2 lines intersect at (3, 1). Consider this system of equations:

y = -1/2x + 2.5
y = 2x - 5
What is the solution to the system of equations?

A) (-5, 0)
B) (2, 0)
C) (3, 1)
D) (4, 3)

Answer 1

The solution to the given system of equations y = -1/2x + 2.5 and y = 2x - 5 is found by equating them and simplifying to find x = 3. Substituting x into one of the equations gives y = 1. Therefore, the solution is (3, 1), which is answer choice C.

Step-by-step explanation:

The student is asking for the solution to a system of linear equations. The given system is:

• y = -1/2x + 2.5
• y = 2x - 5

We can solve this system by setting the two equations equal to each other since they both represent y:

-1/2x + 2.5 = 2x - 5

By adding 1/2x to both sides and adding 5 to both sides to combine like terms, we get:

2.5 + 5 = 2x + 1/2x

Which simplifies to:

7.5 = 2.5x

Now, by dividing both sides by 2.5, we find the value of x:

x = 3

Substituting x back into one of the original equations to find y, let's choose y = 2x - 5:

y = 2(3) - 5

y = 6 - 5

y = 1

So, the solution to the system of equations is (3,1), which corresponds to answer choice C.