Question

How many solutions are there to the following system of equations?

2x – y = 2
–x + 5y = 3

A. infinitely many

B. 2

C. 1

D. 0

Answer 1

Steps:
1. Use either the elimination or the substitution method. (find x)

Answer 2

OR
if the slope of an equation is the negative reciprocal of the other equation. they have 1 solution

Answer 3

if the slopes are the same and have the same y-intercept. it has inifinitely many solutions

Answer 4

if the slopes are the same, but the y-intercepts are not equal, they are parallel whcih means they have no solution

Answer 5

http://www.wolframalpha.com/input/?i=plot+2x+%E2%80%93+y+%3D+2+plot++%E2%80%93x+%2B+5y+%3D+3+

Answer 6

So, that would mean that they had no solution, correct? (I'm really bad at this stuff)

Answer 7

you want me to explain the elimination and substitution?

Answer 8

for Elimination:
1. you need to find the term that you can eliminate easily

Answer 9

in this case, the x.
Multilply the 2nd equation by 2.
You will have

2x – y = 2
–2x + 5y = 3

Answer 10

then you add them.

The term that has x will cancel out.
you will be left with the term that has y and the constant term

Answer 11

then find the value of y:
9y=8

Then, Substitue the value of y to the original equation to find x.
I suggest you substitute the y in both equation,
If you get the same value of x, it has only one solution