Question

help please i dont get this ): Solve the following system by using graph paper or graphing technology.

–3x + y = 2
–9x + 3y = 6

What is the solution to the system?

Answer 1

The first equation contains two variables, so there is not "one" solution. The solution is actually a line! Likewise the second equation contains two variables, so there is not "one" solution. The solution is actually a line!

But if the two lines intersect, then there is "one" solution!

Answer 2

How do you show where the two lines meet? Well, they don't want you to solve it using algebra, but rather, a graph. So graph the first line, graph the second line, and see where they meet.

Answer 3

I am really confused –3x + y = 2 and –9x + 3y = 6 i know i have to make them in "y=mx+b" form but i keep doing it wrong

Answer 4

If you don't want to use algebra, http://www.wolframalpha.com and paste in your formula to check your answer. See "alternate form" where y = mx + b

Answer 5

but i want to know how to do it @maxpolk

Answer 6

For the first you have -3x + y = 2. To get y by itself, move -3x to the other side of the equals sign. We know that from rules of algebra you can always add the same value to both sides of an equals sign. So to "get rid of" the -3x you have to add it's opposite which is +3x.

Hence:
-3x + y = 2
-3x + y + 3x = 2 + 3x
y = 2 + 3x
y = 3x + 2

Answer 7

For the second you have -9x + 3y = 6, so you have to "get rid of" the -9x from the left side (so you add the "opposite" to both sides +9x), then you have 3y and you have to "get rid of" the 3 (so you divide both sides by 3).

Hence:
-9x + 3y = 6
-9x + 3y + 9x = 6 + 9x
3y = 6 + 9x
3y / 3 = (6 + 9x) / 3
y = 2 + 3x
y = 3x + 2

Answer 8

Looks like both of the two equations are saying the same thing a different way.

Answer 9

im still confused how to solve it but i know the answe is Infinite Solutions right?

Answer 10

When you have two variables and only commit to a single statement about them, namely, y = 3x + 2, then when one changes, the other changes. The solution is a line, rather than a single value, so yes, the truth of the single statement (y = 3x + 2) means if x is 1 then y will be 5, and if x is 2 then y will be 8, and so forth. So y has no single value, it depends on x.

Answer 11

im sorry i dont understand that

Answer 12

When someone says y = 3x + 2, they are expressing a relationship between x and y. As x changes, y changes. There is not "one" answer, because x can take on any value. If x is 1 then y will be 5. If x takes on a new value of 2 then y will be 8. Since x can take on any value, there is not "one" answer.

Answer 13

oh okay i kind of get it now