Question

Solve the following system of equations:

x − 2y = 6
2x − 4y = 10

Infinitely many solutions
No solutions
(0, 0)
(6, 10)

Answer 1

solve by what method used ? or indifferent ?

Answer 2

We can multiply both sides of the first equation by 2 to go from
x − 2y = 6
to
2x - 4y = 12

The original system of equations becomes
2x - 4y = 12
2x - 4y = 10

Now let z = 2x - 4y
Replace every copy of 2x-4y with z and we end up with this final system
z = 12
z = 10
But z could only be one number at a time. It cannot be both 12 and 10 at the same time.

This is another way to see why there are no solutions.

Answer 3

@payton still need help?? and what is this lesson called

Answer 4

solving systems of equations

Answer 5

ok still need help??

Answer 6

yeah

Answer 7

ok hold on

Answer 8

Looking at these equations we should realise that there is a problem

The left hand side of each equation is the same, but the right hand sides are different. Huh?

We cannot do the same operations with the variables, but get two different results..

Answer 9

x−2y=6 and x−2y=5 It follows that: if x−2y=x−2y

Answer 10

6=5
is clearly a false statement and there are no variables to solve for.
This tells us that the equation cannot be solved and there are no solutions

Answer 11

make since??

Answer 12

You guys are all doing different formulas and different things. you should work together

Answer 13

\(\color{#0cbb34}{\text{Originally Posted by}}\) @ramen
You guys are all doing different formulas and different things. you should work together
\(\color{#0cbb34}{\text{End of Quote}}\)
true

Answer 14

What everyone is basically saying is that when you substitute x into x, for example x=2y+6 and 2x-4y=10 and you put 2(2y+6)-4y=10 and solve for this, the equation isn't true, for example 12 doesn't equal 10. If the equation ends with a false statement then you know that there's no solution.

Answer 15

@payton you get it now??

Answer 16

yay