Solve the system 2x-4y = 5    x+3y = 7

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We have the two equations 2x-4y = 5 and x+3y = 7 to solve for x.

x+3y = 7 can be rewritten in terms of x as x = 7 - 3y.

Now substitute x = 7 - 3y in 2x-4y = 5

=> 2( 7 - 3y) - 4y...

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We have the two equations 2x-4y = 5 and x+3y = 7 to solve for x.

x+3y = 7 can be rewritten in terms of x as x = 7 - 3y.

Now substitute x = 7 - 3y in 2x-4y = 5

=> 2( 7 - 3y) - 4y = 5

=> 14 - 6y - 4y = 5

=> -10y = 5 - 14

=> -10 y = -9

=> y = 9/10

As x = 7 - 3y

=> x = 7 - 27/10

=> x = (70 - 27)/10

=> x = 43/ 10

Therefore x= 43/10 and y = 9/10

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2x - 4y = 5 ............(1)

x + 3y = 7 .............(2)

We will use the elimination method to solve for x and y.

We will multiply (2) by -2 and add to (1).

==> 2x -4y = 5 ..............(1)

==> -2x - 6y = -14 ............2*(2)

==> -10y = -9

==> y = 9/10 = 0.9

Now to find x we will substitute into (2).

==> x = 7 - 3y = 7- 3(0.9) = 7- 2.7 = 4.3

==> x = 4.3

Then, the solution to the system is the pair ( 4.3 , 0.9)

Approved by eNotes Editorial Team