Question

Solving using substitution, medal for help.

2x + 5y = 27
x + y = 12

Answer 1

Don't give the answer, I'd like to know how to work it out.. :(

Answer 2

rewrite the 2nd equation

x + y = 12

making y the subject..... then substitute into the 1st equation

Answer 3

So y = 12 + x ?

Answer 4

nearly...

to make y the subject you need to subtract x from both sides of the equation.

so

y = 12 - x

does that make sense..?

Answer 5

Since you moved x to the other side, it has to be the opposite. So it's negative x, right?

Answer 6

Since I did that, I have

2x + 60 - 5x = 27

Answer 7

thats correct...

now substitute into the 1st equation

2x + 5(12 - y) = 27

so you need to distribute the 5 as the 1st step

then collect like terms...

is that ok..?

Answer 8

yep... thats perfect...

now collect the like terms..

Answer 9

oops my mistake

its 2x+ 5(12 - x) = 27

Answer 10

This is what I did:
2x + 5 ( 12 - x ) = 27
2x + 60 - 5x = 27
2x + 5x = 27 + 60
7x = 77
7/7 = 77/7
Leaving me with x = 11

Answer 11

not quite.... you need to take care with collecting like terms

2x -5x + 60 = 27

-3x + 60 = 27

Answer 12

But it's plus 5.. :(

Answer 13

Never mind, I see where it's -3x..

Answer 14

yes it \[5 \times (-x) = -5x\]

multiplying a positive and negative results in a negative answer

Answer 15

so is my x & y value (1,-11) ?

Answer 16

ok... so the next step is to do the opposite of + 60 to both sides of the equation...

so subtract 60 from both sides...

-3x + 60 = 27
-60 -60
---------------------
-3x = -33

now divide both sides by-3 to get the x value...

Answer 17

It's .. positive 11....

Answer 18

That was exactly what I got the first time.. :I

Answer 19

yep... its more about getting the process right

your 1st answer

7x = 27 + 60

which should have been

7x = 87

x = 12 3/7

but remember the process for solving an equation... is do the opposite

to find y just substitute your x value into the 2nd equation

Answer 20

hope it helped