Question

Linear equations by substitution 2x-3y=24 2x+y=4

Answer 1

Answer:

x =  4 $\frac{1}{2}$    and         y = -5

Step-by-step explanation:

2x-3y=24  --------------------------------------------------(1)

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

We are to solve using substitution method.

From equation (2),

2x + y = 4

subtract 2x from both-side of the equation

2x - 2x + y = 4 - 2x

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

Substitute equation (3) in equation (1)

2x-3y=24

2x - 3(4 - 2x) = 24

2x - 12 + 6x = 24

8x - 12 = 24

Add 12 to both-side of the equation

8x - 12 + 12 = 24 + 12

8x = 36

Divide both-side of the equation by 8

8x/8 = 36/8

x = 9/2  =  4 $\frac{1}{2}$

Substitute x = 9/2 in equation (3) to get the value of y

y = 4 - 2x

   = 4 - 2($\frac{9}{2}$)

   = 4 - 9

   = -5

y = -5

x =  4 $\frac{1}{2}$    and         y = -5

Answer 2

Answer:

x = 4.5

y = -5

Step-by-step explanation:

2x - 3y = 24                   2x + y = 4

                                      y = -2x + 4

2x - 3(-2x + 4) = 24        y = -2(4.5) + 4

2x - (-6x + 12) = 24         y = -9 + 4

2x + 6x - 12 = 24            y = -5

8x - 12 = 24

8x = 36

x = 4.5