# Algebra Problems: solving using systems of equations

#### nikkifi

##### New member
Hi,

I'm currently in college and taking college algebra. We're learning about solving equations by the substitution method and the addition method. If I could throw 2 problems out there and what I've done so far, maybe someone could help me break them down and finish working them out?

Problem 1: Find the equation, in standard form, with all integer coefficients, of the line perpendicular to 4x - 2y = 10 and passing through (8,5). I'm completely lost on this and don't even know where to begin.

Problem 2: Solve the system of equations using the substitution method. If the answer is a unique solution, present it as an ordered pair: (x,y). If not, specify whether the answer is no solution of infinitly many solutions.
2x + y = 7
9x + 2y = -1

I took the 1st equation to solve then figure into the second. 2x + y = 7
y = -2x + 7
Sadly, I am so lost in this class that is all I was able to come up with.

If anyone can help, I would greatly appreciate it.

Thank you.

#### galactus

##### Super Moderator
Staff member
For #1, you could solve your equation for y. Knowing the line is

perpendicular means its slope is the negative reciprocal.

Then set up your equation with the known data and solve for b.

$$\displaystyle 4x-27=10$$

Solve for y:

$$\displaystyle y=2x-5$$

Now, can you finish using the hints I gave you?.

For the 2nd problem:

You could solve the first equation for y:

$$\displaystyle y=7-2x$$

Sub into the 2nd:

$$\displaystyle 9x+2(7-2x)=-1$$

Now, solve for x. y will follow.

#### nikkifi

##### New member
Thank you

Thank you very much. That did help. I'm so happy I found this site. I have 5 weeks left of this class and this will definitely be a resource I utilize frequently!! Thanks again!!!