Question

hi, could you help with linear function equations, like this problem?
y=2x+5 and y-1=2(x-3) Point of intersection?( , )

Answer 1

Well, you can do it by graphing, substitution, elimination, a matrix... several ways.

Answer 2

i tried but i really don't understand

Answer 3

our teacher doesn't want us to solve by using graphs, and matrixes,

Answer 4

OK. you have these:
y=2x+5
y-1=2(x-3)

That first equation can be said to mean y in terms of x. So you have a value of y. So, use that to do substitution in the second equation.

y-1=2(x-3)
becomes:
(2x+5)-1=2(x-3)

Now solve for x. Once you have x, plug it in and find y.

Answer 5

so i got : 2x+5-1=2x-6
2x+4=2x-6
so do I subtract 2x from both sides?

Answer 6

@e.mccormick

Answer 7

Interesting. Looks like they may be parallel lines.

Answer 8

4=-6 is not true, which means no solution. In 2 variables, no solution is parallel lines.

So, lets confirm another way. paralle lines have the same slope.

Answer 9

i understand that but i have to give the x and y values

Answer 10

y=2x+5 Slope is 2

y-1=2(x-3)
y=2(x-3)-1
y=2x-6-1
y=2x-7 Slope is 2

They are parallel lines.

The slope is the same and the intercepts are different. There is no solution.

Answer 11

For this particular one, do the work to show the slope is the same and the intercepts are different, then put in no solution. Or do the substitution that leads to 4=-6 and say that is wrong and no solution. Either way, you are proving there is no solution which is the only proper answer for this.

Answer 12

okay thanks a lot

Answer 13

No problem! Getting no solution is not the same as no answer. You will be answering your teacher, which is one thing they want, and you will show understanding that not all lines meet, which is another thing they want.