Question

In the system of equations
{ x+2y=5 }
{ 4x-6y=9 }
What does x equal and why?

Answer 1

Hey!

Hope this helps...

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To find what any one variable equals, you must find what the other variable equals too!

First, we are going to find y, substitute it for y to find x...

x + 2y = 5

2y = 5 - x

y = (5-x)/2

Solve for x:

4x - 6y = 9

4x - 6((5-x)/2) = 9

4x - 3(5-x) = 9

4x - 15 + 3x = 9

7x - 15 = 9

7x = 24

x ~ 3.42857... ROUNDED TO 3.43

To know the why, just look at the way this was solved...

Solve for y:

4x - 6y = 9

4(3.43) - 6y ~ 9

13.714 - 6y ~ 9

-6y ~ -4.714

y ~ 0.785 ROUNDED TO 0.79

CHECK:

4x - 6y = 9

4(3.43) - 6(0.79) = 9

13.714 - 4.714 = 9

9 = 9 TRUE

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The symbol ~ means estimated value...

Answer 2

x+2y = 5 , x = 5 - 2y........(substitute in the second equation)

4(5-2y) - 6y = 9 , 20 - 8y - 6y = 9 , 20 - 14y = 9 , y = 11/14

x = 5 - 2y = 5 - 2(11/14) = 24/7