Expert: Bobby Soltani - 8/14/2009

Question
Hi i am going into geometry this year and i have a review packet to do for the first day of school but i dont remmber how to do some of the problems i hope you can help. the first one is how to solve for the given variable:
  solve for y: 3x+5y= 15
the answer is y= -3/5x+3

My other question is it says to solve:
   x+2y= -1
  4x+3y= -9
i know the answer is (-3, 1) but i am not sure how to solve it
Thank you so much!

Answer
Hi Tiffany,

The trick to the first one is to perform steps on both sides of each equation to isolate the variable you are solving for.

3x + 5y = 15
subtract 3x from both sides to get rid of the 3x on the left side of the equals sign.

5y = -3x + 15
divide both sides by 5 to isolate the y on the left side (i.e., (5y)/(5) = y)

y = (-3/5)x + 3

For the second one, these types of problems may generally be referred to as "two equations, two unknowns," and there are several ways to solve them.  One way is by substitution.  Here's how to do it.

(1) x+2y= -1

(2) 4x+3y= -9

Solve the first equation for x by subtracting 2y from both sides

x = -2y - 1

substitute -2y - 1 in for x in equation (2)

4(-2y - 1) + 3y = -9

now we have one equation with one variable, so we can solve for y.

-8y - 4 + 3y = -9

-5y - 4 = -9

-5y = -5
y = 1

now we can substitute 1 in for y in either equation, and we get x = -3.

Let me know if you have any questions.  Good luck with geometry.

Bobby