Question

I need help with this ASAP!

Answer 1

1) (3,5)

2) infinite solutions

Explanation:

1) sketch two lines:

Line 1: joining

(0,-4) and (1,-1)

Line 2: joining

(0,2) and (-2,0)

They will meet at (3,5)

3x - 4 = x + 2

2x = 6

x = 3

y = 5

2) sketch two lines:

Line 1: joining

(2,0) and (5,1)

Line 2: joining

(2,0) and (5,1)

These are two overlapping lines,

So infinite solutions

Answer 2

Answer and Step-by-step explanation:

1) If you graph the lines, you will get the lines in the first attachment. You will see that the intersection point is (3, 5), which is the solution to that system.

2) First, let's convert both of these into slope-intercept form so that they're easier to graph.

x - 3y = 2

x = 3y + 2

3y = x - 2

y =
`(1)/(3)x-(2)/(3)`

AND

-3x + 9y = -6

9y = 3x - 6

y =
`(3)/(9) x-(6)/(9) =(1)/(3) x-(2)/(3)`

We see that these two lines are exactly the same, which means that no matter what coordinate works for one, it will work for the other. In other words, there are infinitely many solutions.

And, if you graph these lines, you will get the graph in the second attachment, where they are the same line.

Hope this helps!