Roller Linear

Roller Linear
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HELP!! PLEASE HURRY i don't know how to solve this stuff! I need to know it to GRADUATE!?

Graph and check to solve the linear system.

4x-y=3
3x+y=4

Use the substitution method to solve the linear system

-2x-5y=7
7x+y=-8

Use linear combinations to solve the linear system

2x+y=0
5x-4y=26

I just need the steps to solve these different kinds.

Also how would i find the answers for these story problems

You have 50 tickets to ride the Ferris wheel and the roller coaster. If you ride 12 times, using 3 tickets for each ferris wheel ride and 5 tickets for each roller coaster ride, how many times did you go on each ride?

You spend $13 to rent five movies for the weekend. since new releases rent for $3 and regular movies rent for $2 how may regular movies did you rent? How many new releases did you rent?

HELP!! PLEASE HURRY i don't know how to solve this stuff! I need to know it to GRADUATE!?
1. Graph and check to solve the linear system.

4x-y=3
3x+y=4
First, solve both for y which will put the equations in slope-intercept form – easier to graph.
y=4x-3
y=-3x+4
Graph both of them and you want to find the point where they intersect. You can see on your graph they intersect at (1, 1). If you have a graphing calculator (TI-83), you can graph, CALC, option 5 (intersect) and find it that way, too.

2. Use the substitution method to solve the linear system

-2x-5y=7
7x+y=-8
Pick the easiest variable to solve for. In this case, y in the second equation because it has no coefficient (number in front of it). So y=-7x-8. Now plug this y into the first equation:
-2x-5(-7x-8)=7 Can you see how that worked? Now, solve this equation for x.
-2x+35x+40=7 (distribute the -5)
33x+40=7 (combine like terms)
33x=-33 (subtract 40 from both sides)
x=-1 (divide both sides by 33)

Now, plug -1 into EITHER of your original equations:
-2(-1)-5y=7 Now, solve for y.
2-5y=7
-5y=5 (Subtract 2 from both sides)
y=-1 (divide both sides by -5)

3. Use linear combinations to solve the linear system

2x+y=0
5x-4y=26

Pick a variable that either has one as its coefficient or in both equations have factors in common. The first equation, y has a coefficient of 1 (perfect). Otherwise, look for numbers like 3 and 9 or 2 and 6 in front of the same variable in your two equations.
You are trying to get rid of that variable. Can you see the y has a coefficient of 1 in the first equation and -4 in the second? Let’s multiply the first equation by 4. what that will do is make the y have 4 as a coefficient, while the other y will still have -4.
Watch:
4[2x+y=0]
5x-4y=26
Becomes:
8x+4y=0
5x-4y=26 (I left the second equation alone.)
Now, add the equations together…
8x+4y=0
+ 5x-4y=26
13x=26 (Now you can solve for x, x=2)
Now plug x=2 back into EITHER equation to solve for y.
In the first equation, 2(2)+y=0, so y=-4.

I just need the steps to solve these different kinds.

Also how would I find the answers for these story problems

4. You have 50 tickets to ride the Ferris wheel and the roller coaster. If you ride 12 times, using 3 tickets for each ferris wheel ride and 5 tickets for each roller coaster ride, how many times did you go on each ride?

Let x be the number of times you rode the ferris wheel, and y be the number of times you rode the roller coaster. If you rode 12 times total, x+y=12. Now, if it takes 3 tickets to ride the ferries wheel, then if you ride x times, you use 3x tickets. Same for the roller coaster, you use 5y tickets. If you use all 50 tickets, then 3x+5y=50. So you now have two equations and you can solve using one of the previous methods.
x+y=12
3x+5y=50
You should get x=5 (ferris wheel rides), y=7 (roller coaster rides)

5. You spend $13 to rent five movies for the weekend. since new releases rent for $3 and regular movies rent for $2 how may regular movies did you rent? How many new releases did you rent?

Let x be the number of new release movies and y be the number of regular movies. How many did you rent altogether? 5, so x+y=5. Now, regular movies cost $2 and new releases are $3. So say you rent x movies at $3 a piece, you spend $3x, right? So another equation will be $3x + $2y = $13. Now, you have two equations you can solve, pick one of the methods above:
x+y=5
2x+3y=13
When you find x, that’s how many new releases and y is how many regular movies.

BTW, x=3 (new releases), y=2(regular)

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