Question

Solve the following system of equations:
x − 2y = 6
2x − 4y = 10

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

Answer 1

first step: multiply the first equation by 2

what do you get ?
just multiply each term by 2

Answer 2

X-4Y=12?

Answer 3

you haven't multiplied the x by 2

Answer 4

x2

Answer 5

2x


giving 2x - 4y = 12

so we have 2 equations

2x - 4y = 12 and
2x - 4y = 10


- do you notice anything odd about these 2 equations?

Answer 6

the 2 left sides are the same but the right ones are different

Answer 7

ok

Answer 8

so are there any values of x and y which will fit the 2 equations?

Answer 9

2

Answer 10

what 2 values?

Answer 11

6,10

Answer 12

x = 6 and y = 10?

Answer 13

yes

Answer 14

no
try first one

2x - 4y = 12
2(6) - 4(10) = 12 - 40 = -28 NOT 12

Answer 15

ohhhh

Answer 16

so would there be no solutions

Answer 17

look at the 2 equations again

can the left side be equal to 10 ANd 12?

Answer 18

thats correct its impossible for LHS to be equal to 10 and 12 so NO SOLUTIONS

Answer 19

if we subtract the 2 equations we get
0 = 10
0 =12 which is of course nonsense

Answer 20

Note that by multiplying equation by a constant number does not change the equation. Its basically the same equation .

Answer 21

i see, thank you so much

Answer 22

if we drew the graph of x - 2y = 6 and 2x - 4y = 12 its would be the same straight line.

Answer 23

yw