Homework help: use elimination to solve each system of equations?

Question

-5x + 3y= 6
x-y=4

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Please include all work

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Please give final answer in coordinates

Answer 1

-5x + 3y= 6
x-y=4

First of all, with this system of equations, I would use substitution, but if the instructor is REQUIRING elimination on this, see below.

You select which variable to eliminate, since neither variable in the second equation has a coefficient, it really doesn't matter. You then multiply the entire 2nd equation by the opposite of the coefficient of the variable that you want to eliminate in the first equation...see below
(I will eliminate x.)
-5x + 3y= 6 ---> the coefficient of x is -5, so the opposite is 5
x-y=4 --->multiply this equation by 5

5(x-y=4) = 5x - 5y = 20

Your new system of equations is:
-5x + 3y= 6
5x - 5y = 20

Now add these equations:
-5x + 3y= 6
5x - 5y = 20
-----------------
0x - 2y = 26 (The 0x goes any, since 0 times anything is 0.)

Now your equation is:
-2y = 26

Divide both sides by -2
-2y/-2 = 26/-2
y = -13

Plug this value back into one of the original equations as the value of y & solve it for x.
x-y=4 ----> x - (-13) = 4
x + 13 = 4 (subtract 13 from both sides)
x = -9

Answer - (-9, -13)

FYI - Below I have solved it using substituion...
-5x + 3y= 6
x-y=4

Solve the 2nd equation for x:
x-y=4
x-y+y=4+y (add y to both sides)
x = 4 + y
Now plug this value into the other equation for the value of x
-5x + 3y= 6
-5(4 + y) + 3y= 6
Multiply it out & simplify it...
-20 - 5y + 3y = 6
-20 -2y = 6 (add 20 to both sides)
-2y = 26 (divide both sides by -2)
y = -13
This value can now be plugged into either of your original equations as y to solve for x.
x-y=4 ----> x - (-13) = 4
x + 13 = 4 (subtract 13 from both sides)
x = -9

Answer - (-9, -13)

Answer 2

Okay, you have to decide whether to eliminate the 'x' or the 'y.' I'll choose 'y'. You can see that one equation has 1 y and the other has 3, so you have to make those equal so you can get rid of them. To do this, multiply the bottom equation by 3. This would give you:
-5x + 3y = 6
3x - 3y = 12

Now combine the two. The positive and negative 3y's will cancel each other out. That leaves you with -2x = 18. Now divide by -2 to get that x by itself, and you have x = -9.

To find y, plug in the value of x to one of the equations.

-5(-9) + 3y = 6
45 + 3y = 6
Subtract 45 from both sides.
3y = -39
Now divide by 3 to get that y by itself.
y = -13

Answer is (-9, -13)

Answer 3

ok.. here we go,..

Lets solve for y by eliminating x

look at the second line

x-y=4... if we switch things around a bit by moving the -y we can change it to

x= y+4

ok.. now we know what x is equal to in terms of y so lets drop it into the top equations...'

-5(y+4) + 3y = 6 (see how that was done? We replaced the x with the Y value)

now we simplify..

-5y - 20 +3y =6 (watch your signs on the first value)

simplify some more

-5y _3y = 20 + 6: or -2y = 26

so y = -13

plug that back into the second equation: x-(-13) = 4

or x+13=4

or x= -9

check it (you DO check your work - right?) by dropping both values into the top equation

-5(-9) + 3(-13) = 6 (simplifying again....)

45 + -39 = 6 (which looks ok to me so we have the answers) in coordinate form: (x,y) :

(-9,-13)

ok... ?