solve the system:    2x-5y= 3     x+ 4y = 8

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First, we can say that x = 8 - 4y.  Then we can substitute that into the first equation.

Once we have done that, we can make the following new equation:

2 (8 - 4y) - 5y = 3

This becomes

16 - 8y - 5y = 3

By subtracting...

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First, we can say that x = 8 - 4y.  Then we can substitute that into the first equation.

Once we have done that, we can make the following new equation:

2 (8 - 4y) - 5y = 3

This becomes

16 - 8y - 5y = 3

By subtracting 16 from both sides, we get

-8y - 5y = -13

or

-13 y = -13

By dividing both sides by -13, we get

y = 1

Now we substitute that back into the first equation and we get

x + 4 = 8

or

x = 4

 

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2x-5y = 3...........(1)

x+ 4y = 8............(2)

We will use the substitution method to solve.

Let us rewrite eq. (2):

x+ 4y = 8

==> x= 8-4y

Now substitute x value in eq. (1):

2x-5y = 3

==> 2(8-4y) - 5y = 3

Open brackets:

==> 16 - 8y - 5y = 3

==> -13y = -13

==> y= 1

but x= 8- 4y

==> x= 8- 4*1 = 4

==> x= 4

Approved by eNotes Editorial Team