Question

16. How many solution does the following system have?

5x-2=y
3x+1=4y

Answer 1

@DanJS

Answer 2

oh wait I forgot to put the answers done

Answer 3

a. one solution
b. two solutions
c. infinitely many solutions
d. no solutions

Answer 4

@wio come backkk D:

Answer 5

Okay, do you know how to solve it?

Answer 6

no :(

Answer 7

simple way to check, first put them both into

ax+by = c form

Answer 8

if you can multiply one equation by a constant number and get the same left hand side, the lines are parallel (no solution) if you can multiply and get the same left and right sides, they are the same exact line, dependent, and have infinitly many solutions

Answer 9

Substitute:\[
5x-2=y
\]Into\[
3x+1=4y
\]for \(y\), to get:\[
3x+1=4(5x-2)
\]Does this make sense?

Answer 10

okay guys.. it makes sense but like I put it in on the desmo and got something but does it mean it would be a many solutions?

Answer 11

5x - 2 = y
3x + 1 = 4y put into ax+by = c form
--------------

5x - y = 2
3x - 4y = -1
--------------

I don't see straight away , a number you could multiply one of the equations by to get the second left side, or both sides, so it probably has ONE solution, and you need to solve for it using one of the few methods.

Answer 12

the easiest was is to sketch them to see whether they interest. if they do not each other then it means there is no solution.

Answer 13

*way

Answer 14

If you solve and get something like

10 = 20, FALSE then it is inconsistent, there are ZERO solutions, parallel lines

or if you get

10 = 10 TRUE then they are dependent, the same line, infinit solutions

Answer 15

*intersect

Answer 16

ohhhh

Answer 17

well you would need a infinite sized window to make sure they didnt intersect from a graph,

you need to make sure they are parallel to decide that they dont intersect, and have no solutions

Parallel, Same Slope, Different Y intercepts
OR
The left side of ax + by is a scalar multiple of cx + dy in the second line

Answer 18

Example,

5x + 10y = 20
15x + 30y = 4

Parallel because 3 time the first left hand side (5x+10y) is the same as the second line left hand side, scalar multiple, parallel lines

Answer 19

If the entire equation is a multiple, on both sides, then Same line Infinite solutions, overlapping, dependent

IE
5x + 10y = 20
15x + 30y = 60

3 times the first equation is the second equation, they are the same line, infinite solutions

Answer 20

ohhh okay

Answer 21

You can always just try to solve, and see what you get,

10 = 10 True means infinite solutions, same line

8 = 6 False means no solutions, parallel lines

x=#, y=# means that is the one intersection, one solution

Answer 22

ohh okay I see now

Answer 23

How can 2 Lines have 2 solutions? that is choice B

Answer 24

without bending one of them

Answer 25

ohh oki thanks guys <3

Answer 26

*Hint* When you only need to know the number of solutions, simply look at the problem.

A first degree equation will have ONE solution:
\[x+5=15\]A second degree equation will have TWO solutions. \[x^2 + 4=20\]A third degree equation will have.. THREE :)

And so forth.