Solve the system by elimination

[4tylers]

Can you look these 3 problems over to see if they are correct.

Solve the system by elimination
4x + 2Y = -8
-4x + 2y = 24
Answer
4x + 2y = -8
4x - 2y =-24
8 = 16
2, -8

-2x + 6y = 20
-2x - 6y = 20
Answer
Always have

Solve the system by substitution
y = 7x - 19
-5x + 5y = -5

Answer
-5x + 5(7x - 19) = -5
4 = 40 -5x + 3 5x - 95 + -5
x= -10 30 - 95 = -5
+ 95 + 75
30 = 90
x = 3, 2

 

[4tylers]

Worked on them again. Are they correct now?

 

[Steven G]

Can you look these 3 problems over to see if they are correct.

Solve the system by elimination
4x + 2Y = -8
-4x + 2y = 24
Answer
4x + 2y = -8
4x - 2y =-24
8 = 16
2, -8

-2x + 6y = 20
-2x - 6y = 20
Answer
Always have

Solve the system by substitution
y = 7x - 19
-5x + 5y = -5

Answer
-5x + 5(7x - 19) = -5
4 = 40 -5x + 3 5x - 95 + -5
x= -10 30 - 95 = -5
+ 95 + 75
30 = 90
x = 3, 2

1st problem: you wrote 8=16. Do you really believe that?

2nd problem: The two equation both start off the same. Then in one equation you add 6x and in the 2nd equation you subtract 6x amd the results are both 20. You think that all values for x and y work. Is 7+2 = 7-2? Is 9+8 =9-8??. In fact if 2 + ? = 2- ? then ?=0. That is 6y =0

4th problem: you wrote 30 = 90. Do you really believe that? Then you wrote x=3,2. Does this mean that x = 2 and x =3?

People makes mistakes all the time, I know I do. But you can't ever write 30=90 or 3=5 as you do know this is wrong. Do not do even do one step in math w/o knowing why it works. If you try to memorize everything it will not work.
Now try to redo the problems again and someone will help you.
I will start you off with the 1st one.

4x + 2Y = -8
-4x + 2y = 24.
Add these two equations.
0x +4y =16 or 4y=16. So y =4 since 4*4=16
Plug in 4 for y in any equation that x and y and solve for x
I will use the 1st equation.
4x + 2(4) = -8
4x + 8 = -8
-8 = -8
4x= -16
x= -4
Solution is (x,y)= (-4, 4)

 

[HallsofIvy]

Can you look these 3 problems over to see if they are correct.

You understand that you can check by plugging the numbers into the equation yourself and see if the work, don't you?

For example, if you meant, in the first problem that x= 2, y= -8, the first equation becomes 4(2)+ 2(-8)= 8- 16= -8 which is correct. The second equation becomes -4(2)+ 2(-8)= -8- 15= -24 which is NOT correct.

Solve the system by elimination
4x + 2Y = -8
-4x + 2y = 24
Answer
4x + 2y = -8
4x - 2y =-24
8 = 16
2, -8

You write "8= 16" which is obviously NOT correct. I presume you intended 8x= 16 but that is wrong. When you add the two equations, 4x+ 4x= 8x and 2y- 2y= 0 (so you have "eliminated" y) but -8- 24= -32, not 16. You have confused addition and subtraction you added on the left but subtracted on the right -8- (-24)= -8+ 24= 16.

-2x + 6y = 20
-2x - 6y = 20
Answer
Always have

I presume you mean that all values of x and y will satisfy these equation but that is wrong.
If you add the two equation -2x+ (-2x)= -4x while 6y+ (-6y)= 0, eliminating y, on the right 20+ 20= 40 so you have -4x= 40, x= -10 so -6x+ 6y= 60+ 6y= 20, 6y= 20- 60= -40, y= -40/6= -20/3. I suspect you have again confused addition and subtraction.

Solve the system by substitution
y = 7x - 19
-5x + 5y = -5

Answer
-5x + 5(7x - 19) = -5
4 = 40

No, 4, is NOT equal to 40! I am sure you know that but I do not know what you were trying to say here.

-5x + 3 5x - 95 + -5

Nor can I see what was intended here.

x= -10 30 - 95 = -5
+ 95 + 75
30 = 90
x = 3, 2

?? You were supposed to find values for x and y, not two values for x! If you meant "x= 3, y= 2, again, you could check yourself. The two equations were y = 7x - 19 and
-5x + 5y = -5. If x= 3 and y= 2, the first equation becomes 2=7(3)- 19= 21- 19 which is correct. the second equation becomes -5(3)+ 5(2)= -15+ 10= -5. Your answer is correct but you working is very difficult to understand.

You were correct in your first step: replacing y in -5x+ 5y= -5 with 7x- 19, from the first equation you have -5x+ 5(7x- 19)= -5 and then 5(7x- 19)= 35x- 95. (So, in "-5x+ 3 5x- 95+ -5" above, you should have had "35x", not "3 5x" and = -5, not "+ -5".)
Now you have -5x+ 5(7x- 19)= -5x+ 35x- 95= 30x- 95= -5. Adding 95 to both sides, 30x= 90, x= 3. Then, y= 7x- 19= 7(3)- 19= 21- 19= 2.