Solving with two variables?

[SimplySophia]

Hi, I'm Sophia. I'm going into my Freshmen year in high school this fall. In 8th grade I took algebra 1 and now I'm doing geometry 4. Over the summer we have a math packet we have to do. For some of the problems on the packet, I'm stuck. Its basically solving for one variable when there are two variables in the expression. For example:

Solve for y: 4x+2y=20 (I just made that up..)

Would it just be y=2x+10, or do I have to get an exact answer for y? And if so, how do I do that? Thanks

 

[SimplySophia]

You were close:
4x + 2y = 20
2y = 20 - 4x
y = 10 - 2x

Stop there!

Google "introduction to equation solving"

Thank You!!

 

[HallsofIvy]

Geometrically, in an xy-coordinate system, 4x+ 2y= 20 and y= 10- 2x represent the same line. ANY point on that line satisfies these equations. Unless there is some other information you cannot identify a specific point (and so a specific y value).

 

[mmm4444bot]

Solve for y: 4x+2y=20

do I have to get [a numerical value] for y?

No.

An instruction to "solve for the variable" generally means "express this variable in terms of the others"; hence, the answer is an algebraic expression versus a Real number.

An instruction to "solve the equation" or "solve the system of equations" is where you need to find Real value(s) for the variable(s) involved.

Cheers :cool: