I've been working on this a while, and I thought I got it right...until I got to step two. When I tried "veryfying my solution point" The lines didn't intersect at (4,2). I don't know, it's probably a silly little mistake on my part, but I can't get it quite right.

The problem is:
1.a)
{2x-3y=2
{3x- y=10
My solution is:
x=4 and y=2
Then I have to put it into intercept form,y=mx+b. I'm pretty sure that this is where I'm messing up. I can't remember which numbers I'm supposed to plug into the formula. I got both,:
eq.1)y=2x-3 eq.2)y=3x-1, and
eq.1)y=4m+2 eq2)y=4m+2 ( i think this is even farther wrong than the last one)
Any help is appreciated! ^^
Thanks.

you solution is correct.

What are you putting into slope intercept form? Both lines that cross at 4,2?
If so, the first line is...
2x-3y=2
-3y=-2x+2
y= 2/3 x -2/3

On the second, 3x-y=10
-y=-3x-10
y=3x+10

I don't know what you are doing.

thank you oh so very much! <3

To verify your solution point, you need to substitute the values of x and y you found into both of the original equations and check if they satisfy the equations.

Let's substitute x = 4 and y = 2 into the first equation:

2x - 3y = 2
2(4) - 3(2) = 2
8 - 6 = 2
2 = 2

The equation is satisfied, so the point (4, 2) is a solution to the first equation.

Now let's substitute x = 4 and y = 2 into the second equation:

3x - y = 10
3(4) - 2 = 10
12 - 2 = 10
10 = 10

Again, the equation is satisfied, so the point (4, 2) is also a solution to the second equation.

Based on this, we can conclude that the point (4, 2) is a valid solution for the system of equations {2x - 3y = 2 and 3x - y = 10}.

As for converting the equations to intercept form (y = mx + b), you need to isolate y in each equation.

For the first equation:
2x - 3y = 2
-3y = -2x + 2
y = (2/3)x - 2/3

For the second equation:
3x - y = 10
-y = -3x + 10
y = 3x - 10

So the intercept form equations are:
First equation: y = (2/3)x - 2/3
Second equation: y = 3x - 10

You can then use these equations to graph the lines and find their point of intersection, which should be (4, 2) as you originally thought.