help with math?

Question

use the substitution method to solve
x = 1/8y -1
y = 1/4 x + 39

Answer 1

The 2nd equation tells you what y is equal to. SUBSTITUTE this "value" (1/4x + 39) in place of the y in the first equation. Then you have: x = 1/8(1/4x + 39).

Distribute the 1/8 and then solve for x.

Answer 2

Replacing the value of y from the second equation in the first one yields

x = 1/8(1/4x+39)-1

= 1/32x+39/8-1

= 1/32x+31/8

<==> (1-1/32)x = 31/8 <==> 31/32x = 31/8 <==> x = 32/8 = 4.

Now replace the value of x in the second equation:

y = 4/4+39 =40.

Thus the solution is {(4,40)}

Answer 3

y=1/4(1/8y-1)+39 x=1/8y-1
y=1/32y-1/4+39 x=1/8(40)-1
y=1/32y+155/4 x=5-1
31/32y=155/4 x=4
y=40 QED



~#41

Answer 4

x = (1/8)y - 1 [1]
y = (1/4)x + 39 [2]

y = 8x + 8 [[3] from [1]]
4y = x + 156 [[4] from [2]]

4(8x+8) = x + 156 [[5] from [4] and [3]]
32x + 32 = x + 156 [[6] from [5]]
31x = 124 [[7] from [6]]
x = 4 [[8] from [7]]
y = 40 [[ from [8] and [2]]

Answer 5

x = 1/8(1/4 x + 39) -1
x = 1/32x + 39/8 - 1
x = 1/32x + 31/38
x - 1/32x = 31/8
32/32x - 1/32x = 31/8
31/32x = 31/8
x = 31/8 * 32/31
x = 4


y = 1/4(1/8y - 1) + 39
y = 1/32y - 1/4 + 39
y = 1/32y + 155/4
y - 1/32y = 155/4
32/32y - 1/32y = 155/4
31/32y = 155/4
y = 155/4 * 32/31
y = 40

Answer 6

y=40, x=4