Question

At what point (x,y) do two lines with equations x-2y=5 and 3x-5y=8 interesect?

Answer 1

\[F. -9,-7\]

Answer 2

\[G. 2, \frac{-7 }{ 2}\]

Answer 3

\[H. -2, \frac{ -7 }{ 2}\]

Answer 4

\[J. -9, 7\]

Answer 5

Hints:

There are two ways to solve this problem, the easy and the hard way:
1. Easy way: substitute each set of answers into the left-hand side of the equations and see if the result equals the right-hand side in both equations. If they are equal, then you've found the right answer choice.
2. Hard way: Solve the system of equations and find out the solution corresponds to which of the answers given.

Why do it the hard way? Because in life, you are generally not given answer choices. Learning the "hard way" will let you solve more real problems.

Good luck!

Answer 6

There are multiple ways to find what point (x,y) the two lines intersect.

*Plug in pairs of x and y, and see if the both equations are both true. Usually this approach should only be used if you already know the answer. It's a good way to double check your work, and although it's possible to find a solution, I wouldn't start with this approach, as it is not very efficient.

*Graph the two lines, and find the point where the two lines intersect. This method works ok when you are able to graph, but this option is not always available.

*Another method is to find what value of x and y satisfy both equations \[x-2y=5\]\[3x-5y=8\]

I think the third method is more useful because all you need is a pencil and paper. There are other methods to find solutions, but these 3 are probably good enough for you current level of mathematics.

Answer 7

@uhhhhhh That's all I needed was a better understanding.

Answer 8

I tried solving using the 3rd method, its not really helping. @uhhhhhh

Answer 9

@Youth which method did you use, substitution, elimination or comparison?

Answer 10

Comparison.

Answer 11

@mathmate

Answer 12

x-2y=5 and 3x-5y=8

Solving by comparison:
We can solve by equating expression y=... and y=... for each equation.
In this case it is not exactly the easiest way to do because we will be involving fractions. If you insist to solve by comparison, you can \(multiply\) instead of divide:
Multiply the first equation by three and express 3x in terms of the rest:
3x-6y=6 => 3x=6y+6
3x-5y=8 => 3x=5y+8
By comparison, we end up with
6y+6=5y+8
from which you can solve for y. Substitute y back into the original equations to solve for x.

Answer 13

Can you break it down at bit more?

Answer 14

Multiply the first equation by three and express 3x in terms of the rest:
3x-6y=6 => 3x=6y+6
3x-5y=8 => 3x=5y+8
By comparison, we end up with
6y+6=5y+8

Are you with me up to here, @Youth ?

Answer 15

Yes. "=>" this was knocking me off.

Answer 16

Oh sorry, it means "implies", or "it follows that".
So can you proceed to solve for y using:
6y+6=5y+8

Answer 17

Ok

Answer 18

Y=2

Answer 19

Good!
Can you now put y=2 into one of the two given equations and solve for x?
This will complete the solution!

Answer 20

I have to go... I'll get it.