Question

Solve the system by substitution
-4.5x-2y=-12.5
3.25x-y=-0.75

Answer 1

Do you know how to isolate a variable?

Answer 2

No

Answer 3

To get the y in the bottom equation isolated, subtract the 3.25x to the other side. This will leave you with -y=.75-3.25x.
Then multiply everything by -1 to get the y positive. This will leave you with y=-.75+3.25x.
After that put the y=-.75+3.25x into the top equation which will get you
-4.5x-2(-.75+3.25x)=-12.5
Should be easy from there

Answer 4

I'm positive I got this wrong, but is it -1.25x-1.25=-12.5?

Answer 5

***
Solve the system by substitution
-4.5x-2y=-12.5
3.25x-y=-0.75
***

"by substitution" means use one of the equations, and "solve" for one of the variables
in this case, the 2nd equation is easiest to use..if we solve for "y"

3.25x-y=-0.75
first, we can add +0.75 to both sides, like this
3.25x+0.75 -y=-0.75+0.75

Answer 6

3.25x+0.75 -y=-0.75+0.75
the right side simplifies to 0. we have

3.25x+0.75 -y= 0
now add +y to both sides:
3.25x+0.75 -y + y=0+y
that simplifies to
3.25x+0.75 = y
or

y = 3.25x+0.75

Answer 7

now you have what y is equal to:
y = 3.25x+0.75

use that expression in the first equation
-4.5x-2y=-12.5 <-- replace y with (3.25x+0.75)

you get
-4.5x-2(3.25x+0.75)=-12.5

now to solve for x, you should think of this as
-4.5x + -2(3.25x+0.75)=-12.5
The first step is "distribute" the -2. that means multiply -2 times each term inside the parens.

Can you do that ?

Answer 8

@Phi do I subtract -4.5x from -6.5x? Or rather add them?

Answer 9

First, after you distribute the -2 , you should get

-4.5x -6.5x -1.5 = -12.5

to avoid confusion, you should change subtraction to "adding negative numbers (or letters)"
in other words, write this as
-4.5x + -6.5x + -1.5 = -12.5
which means the same thing, but makes it more clear (to me anyways) that you add the two negative terms to get an even more negative term...

can you simplify ?

Answer 10

-4.5x+-6.5x+-1.5=-12.5

Answer 11

you should combine the "like terms"

It is easier to see with "nice" numbers: if you had 1x + 2x that means 1 x plus 2 more x's which is 3 x's or 3x

or if you had -1x - 2x that means -1 x take away 2 more x's gives -3 x's or -3x

in your case you have -4.5x+-6.5x
can you combine those two terms ?

Answer 12

I had actually combined them in my head, I just don't know why I didn't type it.

-11x+-1.5=-12.5

Answer 13

too bad, I could have saved all that typing.
now add +1.5 to both sides

Answer 14

-11x+-1.5+1.5=-12.5+1.5

-11=-11

Answer 15

I hope you mean
-11x = -11

Answer 16

now divide both sides by -11

Answer 17

1

Answer 18

1=1

Answer 19

you should write out the whole equation (a good habit, which is helpful to not getting lost for complicated problems)

-11x = -11

\[ \frac{-11}{-11} x = \frac{-11}{-11} \\
x=1

\]

now you need to find y

from way up above, we have this equation
y = 3.25x+0.75
can you find y when x = 1 ?

Answer 20

3.25(1)+0.75=4

y=4

Answer 21

yes, that looks good.

you can always check your answer by replacing x with 1 and y with 4 in the original equations and make sure they are true.

Answer 22

Thank you!!