## Solve linear equations with 2 unknowns

Simplificatation, evaluation, linear equations, linear graphs, linear inequalities, basic word problems, etc.
ironape
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### Solve linear equations with 2 unknowns

Im just not seeing what im doing wrong to solve this. Can anyone take a look and let me know where I am going wrong with it?

4x + 1y = 16
-3(4x + 1y) = -3(16)
-12x + -3y = -48
2x + 3y = -24
-10x + 0y = -24
-10x = -24
-10/-10 = -24/-10
x = -2.4

4(-2.4) + 1y = 16
-9.6 + 1y = 16
(-9.6+9.6) + 1y = (16 + 9.6)
0 + 1y = 25.6
1y = 25.6

y=25.6
x=-2.4

4x + 1y = 16
4(-2.4) + 1(25.6) = 16
-9.6 + 25.6 = 16

2x + 3y = 24
2(-2.4) + 3(25.6) = 24
-4.8 + 76.8 = 72???

Works for one but not the other?

stapel_eliz
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ironape wrote:4x + 1y = 16
-3(4x + 1y) = -3(16)

What are the two original equations? Thank you!

ironape
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### Re: Solve linear equations with 2 unknowns

4x + 1y = 16

2X + 3Y = 24

stapel_eliz
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ironape wrote:4x + 1y = 16

2X + 3Y = 24

From what you'd posted earlier, I think you're trying to solve by substitution...? I will assume that you mean "X" and "Y" to be "x" and "y" respectively, since otherwise the system is not solveable.

Since the first equation can easily solved for "y=", that's probably the way to go.

. . . . .$y\, =\, 16\, -\, 4x$

Then plug this in, in place of "y", in the second equation:

. . . . .$2x\, +\, 3(16\, -\, 4x)\, =\, 24$

Then solve the linear equation for the value of x, and back-solve then for the value of y.

ironape
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### Re: Solve linear equations with 2 unknowns

whats the answer so i can try and figure out what ive done wrong. The way ive worked the problem has been the same for 10 other problems and they all came out right. I just dont know what im missing with this one.

stapel_eliz
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Joined: Mon Dec 08, 2008 4:22 pm
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To figure out where you may have gone wrong, we'll need to see your work. Please dtart from what was given to you earlier, and please provide a clear listing of your steps after that point.

Or, if you prefer to try solving by elimination, try multiplying the second row by $-2$, giving you:

. . . . .$+4x\, +\, 1y\, =\, 16$

. . . . .$-4x\, -\, 6y\, =\, -72$

Please show your work, starting with adding down, and then showing how you solved the resulting linear equation in $y$, etc.

Thank you!

ironape
Posts: 21
Joined: Wed Oct 07, 2009 4:45 pm
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### Re: Solve linear equations with 2 unknowns

Problem: 4x+y=16 2x+3y=24

im going to solve for x since i can easily remove y in the first equation by multiplying by -3

4x + 1y = 16
-3(4x + 1y) = -3(16)
-12x + -3y = -48

I get the above result which i will subtract the second equation from

-12x + -3y = -48
2x + 3y = 24
-10x + 0y = -24
-10x = -24
-10/-10x = -24/-10
1x = 12/5

At this point does x=12/5?

draindrop
Posts: 1
Joined: Thu Oct 22, 2009 4:50 pm
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### Re: Solve linear equations with 2 unknowns

Method 1
__________________________
4x + y = 16 ---- (EQ-A)

y = 16 - 4x

2x +3y = -24 ---- (EQ - B)

Replace the value of Y

2x + 3(16 - 4x) = -24

2x + 48 - 12x = -24

-10X +48 = -24

-10X = -24-48

-10X = -72

10X = 72

X = 72 / 10

X = 7.2----------*

y = 16 - 4(7.2)

y = 16 - 28.8

y = -12.8

vERIFICATION

4X+Y = 16
4(7.2) + (-12.8) = 16
28.8 - 12.8 = 16
16 = 16

2X + 3y = -24
2(7.2) + 3(-12.8) = -24
14.4 - 38.4 = -24

-24 = -24
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

Method 2

4x + y = 16 ------ (equation-A)
2x + 3y = -24 -----(equation-B)

Multiply by -3 to equation A

-3(4x+y) = -3(16)
-12x - 3y = -48 -----(eqation - c)

2x + 3y = -24
-12x - 3y = -48
-------------------
-10x = -72

x = 7.2

put value of "x" in equation A

4(7.2) + y = 16
28.8 + y = 16

y = 16 - 28.8

y = -12.8

vERIFICATION

4X+Y = 16
4(7.2) + (-12.8) = 16
28.8 - 12.8 = 16
16 = 16

2X + 3y = -24
2(7.2) + 3(-12.8) = -24
14.4 - 38.4 = -24

-24 = -24

ironape
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### Re: Solve linear equations with 2 unknowns

The problem is equation B is:

2x+3y = 24 <positive 24>

not

2x + 3y = -24

It doesnt matter because I found where I messed up. I have to be careful when figuring if an answer is negative or positive. I made 2 mistakes which skewed the answers. Inputting the below answers will check out.

x=2.4
y=9.6

Thanks for taking the time to help me out