Question

Determine whether the point (4,2) is a solution set to the system {2x+y=10} {x=y+2}

Answer 1

Answer: yes it is a solution

Step-by-step explanation

The coordinates (4,2) mean that x = 4 and y = 2 pair up together.

Plug them into the 1st equation.

2x+y = 10

2*4 + 2 = 10

8 + 2 = 10

10 = 10

So far so good. Let's check the other equation.

x = y+2

4 = 2+2

4 = 4

This is true as well.

Since both equations are true, it means (4,2) is a solution.

It turns out it's the only solution of the system. It's where the two lines intersect.