How do I solve this Algebra problem?

The lesson that I am learning is: Solve Linear Systems by Adding or Subtracting and I am having some trouble with problem #20

Here it is:

11y-3x=18

-3x= -16y+33

I am getting like a decimal. Any help would be great thanks!

Relevance

reorganize and solve

-3x=-16y+33 becomes 16y -3x = 33

subtract second from first to change sign

11y-3x = 18

16y-3x = 33 subtract

_______________

-5y = -15

y = -15/-5 = 3

substitute back into the equations

-3X = -16(3) + 33

-3X = -48 + 33

-3x = -15

x = 5

check 11(3) - 3(5) = 18

33 -15 = 18

18 = 18

-3(5) = - 16(3) + 33

-15 = -48 + 33 = -15

• Lucy
Lv 7

The answer definitely does not include decimals. Here is how you do it:

Given:

11y - 3x = 18

-3x = -16y + 33

First, write both of these equations so that the variables line up with each other.

-3x + 11y = 18

-3x + 16y = 33

Multiply the first one by -1.

-1(-3x + 11y) = -1(18)

-1(-3x + 11y) = -18

Distribute.

-1(-3x) - 1(11y) = -18

3x - 11y = -18

3x - 11y = -18

-3x + 16y = 33

3x - 11y = -18

-3x + 16y = 33

------------------------------------

5y = 15

Divide both sides by 5.

5y / 5 = 15 / 5

y = 3

Plug this back into one of the equations and solve for x.

-3x = -16y + 33

-3x = -16(3) + 33

-3x = -48 + 33

-3x = -15

-3x / -3 = -15 / -3

x = 5

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

CHECK:

You can always check your answer by plugging in the values you found back into the original equations to find out if both sides equal each other.

11y - 3x = 18

11(3) - 3(5) = 18?

33 - 15 = 18?

18 = 18?

true

-3x = -16y + 33

-3(5) = -16(3) + 33?

-15 = -48 + 33?

-15 = -15?

true

Source(s): For more help on elimination: http://www.purplemath.com/modules/systlin5.htm
• Anonymous

actually you could use the addition by subtraction method

11y-3x=18

-3x= -16y+33

-3x+11y=18

-3x +16y=-33

+ -3x+11y=18

(- ) 3x -16y=-33

-5y=-15

-5 -5

y= 3

then substitute to get the value of x

-3x= -16y+33

-3x= -16(3)+33

-3x= -48+33

-3x=-15

-3 -3

x=5

i would make additional information later i still have my class.. hang on there.. God bless

Well the equation for a slope is y=mx+b. so first off get it to this point by rearranging the equation. b is the plain old number. nothing special about it. the mx part is the x and the m which is the coefficient. so for example 5x would = mx because the 5 is the coefficient. and y is...y. So for the first one you add 3x to both sides and you get 11y=3x+18. Hope I could help.

heres how u solve. put all numbers and variables aligned like this:

16y-3x=33

11y-3x=33

make sure u cancel one of them out. multiply one of them by -1.

16y-3x=33

-11y+3x=-33

16y-11y=5y. x's cancel and so do the regular numbers.

5y=0

plug y in.

16(0)-3x=33

-3x=33

x=11

• Anonymous

-3x + 11y = 18

3x - 16y = -33

-5y = -15

y = 3

-3x + 11(3) = 18

-3x = 18 - 33

-3x = -15

x = 5

11y-3x=18

or

-3x = -11y+18

-3x= -16y+33

Now

-11y+18 = -16y+33

5y = 15

y = 3

Substitute:

x = 5

11y-3(-16y+33)=18

11y-3x=18..............Eq.1

-3x= -16y+33..........Eq.2

Re-organize both equations

-3x+11y=18............Eq.1

-3x+16y=33............Eq.2

-3x+11y= 18...........Eq.1

3x-16y= -33...........Eq.2 X -1

-5y=-15

5y=15

y=3

Substitute 3 for y in either original equation.

I'll use -3x+11y= 18

-3x+11(3)=18

-3x+33=18

-3x=18-33

-3x=-15

3x=15

x=5

Solution is x=5, y=3

• Anonymous