Question

What is the solution of this linear system?
x + 3y = -8
4x − 3y = 23

a) (0, -8/3)
b) (3,-11,3)
c) (4,-4)
d) (7,-5)

please help !

Answer 1

Ok, the answer is b. and I'm going to show you how I got this. Use the addition method of solving equations in 2 variables. In case you don't know how to do that, I'm going to show you. Line one equation up under the other to get this:
x + 3y = -8
4x - 3y = 23
When you look at that, you can see that by adding the columns straight down, the 3y's cancel out because 3y - 3y = 0. So we can cross those out and what we are left with is x + 4x = 23 - 8. Doing the math, you get 5x = 15. Solving for x gives you x = 3. Now fill that 3 back into one of the original equations to solve for y. 3 + 3y = -8; subtract 3 from both sides giving you 3y = -11; divide both sides by 3 and get y = -11/3. Got that? I hope it helped!

Answer 2

so you basically just cancel them out ?

Answer 3

When you do the addition method, in this particular problem, yes, they do cancel out. If they were not the same coefficient with opposite signs, you would have to make them be the same coefficient with opposite signs by multiplying one of them by whatever it takes to get them to be the same number. For example, if you had 3y and 1y, you would have to multiply the 1 y by a -3 to get the y term to change from a 1 to a -3y; when it's a -3y, THEN it will cancel with the positive 3y. BUT if you multiply the 1 by a -3, the whole entire expression that contains the 1y has to be multiplied by -3, not just the 1. Get it? If not, keep asking questions til you understand. I can probably post an example to help you understand.

Answer 4

yeah that makes sense , thanks for help :)