The difference of two numbers is 66. The second is 6 less than 5 times the first. What are the two numbers?

Question

Rewrite the equation y = –5x + 3 as a function of x.

Solve the system by addition.
x + y = 10
x – y = 6

Solve the following system of linear inequalities by graphing.
x – 2y < 4
x <1

Answer 1

(1)
b - a = 66
b = 5a - 6

Substitute the second into the first:

b - a = 66
(5a - 6) - a = 66
4a - 6 = 66
4a = 72
a = 18

b - a = 66
b - 18 = 66
b = 84

The two numbers are 18 and 84

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(2)
y = –5x + 3
5x = -y + 3
x = -y/5 + 3/5

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(3)
x + y = 10
x – y = 6

Add the two equations vertically:

x + y = 10
x – y = 6
-------------
x + x + y - y = 10 + 6
2x = 16
x = 8

Subtract the two equations to solve for y:

x + y = 10
x – y = 6
-------------
x - x + y - (-y) = 10 - 6
2y = 4
y = 2

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(4) x – 2y < 4
x <1

Can't really draw a graph for you in Yahoo Answers.

x < 1 is a dashed vertical line at x=1 shaded to the left.

x - 2y < 4 is a dashed line that goes through (4,0) and (0,-2) shaded to the upper-left of the line.

The overlap of those two areas is the solution.

Answer 2

1) x-y=66, y=5x-6
x-(5x-6)=66
-4x+6=66
-4x=60
x=-15
y=-81

2) y=-5x+3
y-3=-5x
(y-3)/-5=x or (-y+3)/5=x

3) x+y=10
x-y=6

2x=16
x=8
y=2

4) x-2y<4; -2y<-x+4; y>(1/2)x-2
x<1

the first one has a y-intercept at -2, from there apply slope (rise over run) of up 1 and right 2, shade above the line
the second one is a vertical line through x=1 and is shaded to the left

Where the shading overlaps is your "answer". Also, both lines are dotted lines.

Answer 3

Let the first no.=x
so the second no.=66+x
As Per the given condition,we have
66+x=5.x-6
or x-5x=-6-66
or -4x=-72
or x=72/4=18,is the 1st no.
so the 2nd no.will be 66+x=66+18=84
so the no.'s are 18 & 84 ans

Answer 4

let the two numbers are a &b, so the diference is a-b = 66
b is 5a-6
a- (5a-6)=66
-4a+6 =66
-4a=66-6
a=60/-4
a=-15
b=5(-15)-6==>-81


y=-5x+3
y-3=-5x
5x=3-y
x=(3-y)/5


2x=16
x=8
y=2

use the graphical calucator for the last one.

Answer 5

x - y = 66
x = 5y - 6
5y - 6 - y = 66
4y - 6 = 66
4y = 72
y = 18
x = 5(18) - 6
x = 90 - 6
x = 84