Question

1)2x-y=1

2)X +y=5

1)X-y=3
2)2x+4y=12

1)x+y=4
2)2x-y=3

1)x-2y=10
2)4x4y=4

Answer 1

Explanation:

Lets solve each simultaneous equation

1.)

2x – y = 1. ----------(1)

x + y = 5. ----------- (2)

x = 5 – y -------------(3)

just substitute for x in equation (1)

2(5–y) – y = 1

10 – 2y – y = 1

10 – 3y = 1

–3y = 1 – 10

–3y = – 9

divide both sides by (–3)

y = 3

since y= 3 just substitute for equation (3)

x = 5–y

x = 5–3

x = 2

for the first simultaneous equation x=2,y=3

2.)

x – y = 3 ---------(1)

2x + 4y = 12------(2)

x = y + 3 --------(3)

just substitute for x in equation (2)

2(y+3) + 4y = 12

2y + 6 + 4y = 12

6y + 6 = 12

6y = 12– 6

6y = 6

divide both sides by (6)

y = 1

since y=1 just substitute for y in eqn (3)

x = y + 3

x = 1 + 3

x = 4

for the second simultaneous equation x = 4, y = 1

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

2x – y = 3 -------------(2)

x = 4 – y ---------------(3)

just substitute for x in equation 2

2(4–y) – y = 3

8 – 2y – y = 3

8 –3y = 3

–3y = 3 – 8

–3y = –5

divide both sides by (-3)

y = 5/3

substitute for y in equation (3)

x = 4– y

x = 4 – 5/3

multiply both sides by (3)

3x = 12 – 5

3x = 7

divide both sides by (3)

x = 7/3

for the third simultaneous equation x = 7/3 ,y = 5/3

4.) x– 2y = 10 ------------(1)

4x – 4y = 4. -------------(2)

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