Solve the following system of linear equations. Present your solution as an ordered pair (x,y) 3x + 4y = 11 x - 2y = 7

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We have to following set of equations for x and y, 3x+4y=11 and x-2y=7.

3x+4y=11...(1)

x-2y=7...(2)

Now (1) - 3*(2)

=> 3x + 4y - 3x + 6y = 11 - 21

=> 10y = -10

=> y = -10/ 10

=> y = -1

Substitute y = -1 in...

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We have to following set of equations for x and y, 3x+4y=11 and x-2y=7.

3x+4y=11...(1)

x-2y=7...(2)

Now (1) - 3*(2)

=> 3x + 4y - 3x + 6y = 11 - 21

=> 10y = -10

=> y = -10/ 10

=> y = -1

Substitute y = -1 in (2)

=> x - 2*(-1) = 7

=> x = 7 - 2

=> x = 5

Therefore the required solution is (5 , -1)

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3x + 4y = 11 .................(1)

x - 2y = 7 ....................(2)

We are given a system of two equations and two variables.

We will use the substitution method to find x and y values.

First, we will re-write (2).

==> x= 2y+7

Now we will substitute x values in (1).

==> 3x+ 4y = 11

==> 3(2y+7) + 4y = 11

==> 6y + 21 + 4y = 11

==> 10y + 21 = 11

==> 10y = -10

==> y= -1

==> x= 2y+7 = 2*-1 + 7 = 5

==> x= 5

Then, the answer is ( 5, -1).

Approved by eNotes Editorial Team