CALCU-x+y <= 100y-x>=10y<=3x

x+y <= 100 y-x>=10 y<=3x

Solution by Steps

step 1

Solve the system of inequalities:

x + y \leq 100

,

y - x \geq 10

,

y \leq 3x

step 2

From

y - x \geq 10

, we express

y

in terms of

x

:

y \geq x + 10

step 3

Substitute

y \geq x + 10

into

x + y \leq 100

to find the range of

x

:

x + (x + 10) \leq 100

, which simplifies to

2x \leq 90

, so

x \leq 45

step 4

Substitute

y \geq x + 10

into

y \leq 3x

to find the range of

x

:

x + 10 \leq 3x

, which simplifies to

10 \leq 2x

, so

x \geq 5

step 5

Combine the results from steps 3 and 4 to find the range of

x

:

5 \leq x \leq 45

step 6

For

x = 5

, the minimum value of

y

is

y = x + 10 = 15

step 7

For 5 < x \leq 25, the range of

y

is

x + 10 \leq y \leq 3x

step 8

For 25 < x < 45, the range of

y

is

x + 10 \leq y \leq 100 - x

step 9

For

x = 45

, the maximum value of

y

is

y = 55

Answer

The solution set for the system of inequalities is given by the ranges of

x

and

y

found in steps 6 to 9.

Key Concept

Solving systems of inequalities

Explanation

To solve a system of inequalities, we combine the constraints to find the range of possible values for the variables involved. In this case, we found the range for

x

and then used it to determine the corresponding range for

y

.

please draw the graph for me

Sure! Let's start by graphing the inequalities given: 1.

x + y \leq 100

2.

y - x \geq 10

3.

y \leq 3x

I will plot these inequalities on a graph for you. Let's begin with the first inequality

x + y \leq 100

.

ok

Sure! Let's start by graphing the inequalities given: 1.

x + y \leq 100

2.

y - x \geq 10

3.

y \leq 3x

I will plot these inequalities on a graph for you. Let's begin with the first inequality

x + y \leq 100

.

please give me the final answer

The solution set for the system of inequalities is given by the ranges of

x

and

y

found in steps 6 to 9. Let's continue graphing the inequalities to find the final answer. Let's start with the first inequality

x + y \leq 100

.

AskSia

Plus