Question

Solve using the elimination method. If the system has an infinite number of solutions, use set builder notation to write the solution set. If the system has no solution, state this.

x + 9y = 79
-7x + 9y = 23

Answer 1

eliminate y's by multiplying first equation by -1

Answer 2

-x - 9y = -79 would that be right for the first one?

Answer 3

GREAT!

Answer 4

so you should get -8x=-56 right?

Answer 5

how do you get that?

Answer 6

so x=7 plug x into second eqn to get y

Answer 7

the ys cancel and you have -x + -8x and -79 + 23

Answer 8

sorry -x + -7x

Answer 9

oh okay. so you use it to both equations after you solve the first one?

Answer 10

you can pick one equation to plug back into to get the other variable...preferably the one you didn't alter

Answer 11

plug both x and y into both original equations to check

Answer 12

-7-9(8)=-79
-7-72=-79
-79=-79 TRUE

Answer 13

OK. So what do I do after I plug it into the second equation?

Answer 14

-7(7)+9(8)=23
-49+72=23
23=23 TRUE

Answer 15

solve for y then combine (x,y) for solution (7,8)

Answer 16

So, (7,8) would be the answer correct? That's what I got.

Answer 17

GREAT!!!!!

Answer 18

Thank you so much. How would I know if an equation has no solution or infinite solutions?

Answer 19

no solution would give you different numbers on each side of equal side such as -2=0 and infinite solutions would give you same number on each side like 5=5

Answer 20

parallel lines have no solution and same line have infinite solutions so if you put them in y=mx+b form and look at slope (m)-same for parallel

Answer 21

Ok. thanks

Answer 22

welcome...medal or fan me please :)