One number is 3 times another. if the difference of the numbers is 36, find the two numbers.

The two numbers are 18 and 54.

In order to find these, we need to set up a system of equations. To write the first equation, we'll focus on the beginning of this statement. Let x be the first number and y be the second (or "another"). Since x is 3 times y, we can set x = 3y and solve for an equation.

x = 3y > subtract 3y

x - 3y = 0

Now we also know that subtracting y (the smaller number than x), will give us 36.

x - y = 36

Now we can solve the system by multiplying the first equation by -1 and adding together.

-x + 3y = 0

x - y = 36

2y = 36 > divide by 2

y = 18

So we now know that one number is 18, plug back into either equation to find the other.

x - y = 36

x - 18 = 36

x = 54

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be