Question

Beyonce is solving a system of equations: 2x - 3y = - 2 and 4x + y = 24 She multiplies the second equation by 3 and then adds the first equation to find 14x = - 70 showing her that x=5. . Beyonce finds that y=4. Thinking about this process, Beyonce says out loud, " There are lots of ways I could go about solving this problem. I could do the method above or I could multiply the first equation by -2 and add the second . I seem to find that there is only one solution to the two equations but I wonder if I will get the same solution if I use a different method?

Answer 1

Yes, Beyonce will get the same solution.

Explanation:

The given system is

2x - 3y = - 2

and

4x + y = 24

If she multiplies the first equation by -2 , she gets,

-4x+6y=4

4x + y = 24

Adding the two equations gives

7y=28

This means y=4

When we put y=4 into the bottom equation we get:

4x+4=24

4x=20

x=5

Therefore Beyonce will still get x=5, and y=4 as solution.