by elimination 7y + 2x = 5, 2y - x = 3 I have the answers, but need how to work the problem

Question

Also this problem:difference of two numbers is 3 and twice their sum is -4 what are these numbers

Answer 1

The goal is to add the two equations together so that you eliminate one of the variables, either the x or the y.  You are then left with an equation in one variable that you can solve.

 

7y + 2x = 5

2y  -  x = 3

 

It looks easiest to eliminate the x since you have +2x in the top term and -x in the bottom term.  So let's multiply the bottom term by 2 then add:

 

7y + 2x = 5
4y  - 2x = 6

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11y       = 11

 

Can you finish it from here?

 

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Second problem:  The difference of two numbers is 3 and twice their sum is -4.  What are these numbers?

 

Let x = one of the numbers

let y = the other number

 

The difference of two numbers is 3:  x - y = 3

Twice their sum is -4: 2(x+y) = 2x + 2y = -4

 

Solve by eliminating the y variable (hint: multiply the first equation by 2 then add the equations together).

 

Answer 2

First Problem

The trick is to find out what one of your variables is in terms of the other variable, and then solve for that second variable. 

For example 2y-x=3 --> 3 + x = 2y --> x = 2y - 3 now plug this value of 'x' back into the original equation:

7y + 2x = 5 = 2(2y-3)+7y = 5 --> 11y - 6 = 5 --> 11y = 11 --> y = 1. 

Now plug this y value back into your equation for x: x = 2y - 3 --> x = 2*(1) - 3 --> x = -1

So y = 1, x = -1

 

Second Problem

Set Variables x,y to be the two numbers

next write out the two equations-

x-y = 3

2(x+y) = -4

 

Now do the same thing as the first problem- find out what one variable equals in terms of the other:

x - y = 3 --> x = y+3

And plug this value for x into the 2nd equation: 2(y+3) + 2(y) = -4 --> 4y + 6 = -4 --> 4y = -10 --> y = -5/2

and plug this in for your x equation: x = y+3 --> x = -5/2 + 3 = 1/2 = x

 

so y = -5/2 x = 1/2