Question

What is the solution of the following systems of equations?

-none
-infinite
- (5, 7)
-(1, -2)

Answer 1

(1,-2)

Explanation:

The solution refers to the point of intersection of two lines. When we're dealing with straight lines, the possible solutions are:

- None (the lines are parallel - have the same slope - so they never instersect)

- Infinite (the lines are parallel and on top of each other so they intersect at every point)

- One point of intersection (the lines have different slopes)

The graph provided shows lines with two different slopes, so they must intersect at one point. We know the answer is one of the two points provided. Looking at the graph, you see the point of intersection, or the solution, is (1, -2).

You can check this by solving the system mathematically. The point of intersection is a point that satsifies both line equations. Start by solving for x as y is isolated:

`3x-5 =-x-1\\4x=4\\x=1`

Now use the calculated x-value to solve for y in either equation (I'll use the first):

`y=3(1)-5\\y=3-5\\y=-2`

The solution is (1, -2).