Question

Find the solution to the following system of linear equations:

3/2x-2y=4

x+1/3y=2

Answer 1

x = 32/15 and

y = - 2/5

Explanation:

a) 3/2x-2y=4

b) x+1/3y=2

Elimination:

b) -1/3(x+1/3y=2) = -3/2x - 1/2y = -3

a+b = (3/2x-2y=4) + (-3/2x-1/2y=-3)

= -5/2y = 1

y = 1/(-5/2

y = -2/5

Substitution:

a) 3/2x -2(-2/5) = 4

3/2x +4/5 = 4

3/2x = 4 - 4/5

x = (-16/5)/(3/2)

x =32/15

Answer 2

x = 13/20

y = 11/40

Explanation:

3 / 2x - 2y = 4 (1)

x + 1 / 3y = 2 (2)

by simplifying equation (1)

3 = 4(2x - 2y)

3 = 8x - 8y (3)

by simplifying equation (2)

x + 1 = 2(3y)

x + 1 = 6y

x - 6y = -1 (4)

by multiplying equation (4) by 8

8x - 48y = -8 (5)

by subtracting equation (3) from equation (5)

8x - 48y = -8

8x - 8y = 3

- + -

___________

-40y = -11

y = 11/40

by substituting value of y in equation (4)

x - 6(11/40) = -1

x = -1 + 66/40

= -40 + 66 / 40

= 26/40 = 13/20

x = 13/20