Question

consider the following system of equation 8x+4y=20. 2x-y=4. suppose the second line of the original system is replaced with the sum of the two lines. determine if the solution of the new system is the same as the original system

Answer 1

The original system of equation is:

8x + 4y = 20................(1)

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

To solve the system of equation above, multiply equation (1) by 1 and equation (2) by 4

The system of equation becomes:

8x + 4y = 20.........(3)

8x - 4y = 16..........(4)

Add equations (3) and (4)

16x = 36

x = 36 / 16

x = 9 / 4

Put the value of x into equation (2)

2 (9/4) - y = 4

y = 9/2 - 4

y = 1 / 2

If the second line of the original system is replaced with the sum of the two lines

Equation (2) of the original system becomes:

(8x + 4y) + (2x - y) = 20 + 4

10x + 3y = 24

Equattion (1) does not change for the new system of equation:

The new system of equation is therfore:

8x + 4y = 20..............(1)

10x + 3y = 24..............(2)

Multiply equation (1) by 3 and equation (2) by 4

24x + 12y = 60...........(3)

40x + 12y = 96.............(4)

Subtract equation (3) from equation (4)

16x = 36

x = 36 / 16

x = 9 / 4

Put the value of x into equation (1)

8 (9 / 4) + 4y = 20

18 + 4y = 20

4y = 20 - 18

4y = 2

y = 2 / 4

y = 1/2

For the old system of equation: x = 9/4 , y = 1/2

For the new system of equation: x