One number added to three times another number is 24 . five times the first number added to three times the other number is 36 . find the numbers

First number = 3

Second number = 7

Step-by-step explanation:

Let one number be =

Let other number be =

"One number added to three times another number is 24" can be written mathematically as:

Five times the first number added to three times the other number is 36 can be written mathematically as:

So, we have a system of equation as:

A)

B)

Solving for and using elimination.

Multiplying equation A with -1 and adding it to B to eliminate

would be

would be

+  

We have,

Thus is eliminated. Now, we can solve for

Dividing both sides by 4.

∴

Plugging in in equation A to solve for

Subtracting both sides by 3.

Dividing both sides by 3.

∴

So, first number = 3

Second number = 7

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is