Two Variables Inequalities



Two Variables Inequalities

Question # 68

Solution

Y1 = 330

Y2 = 0

X1 = 0

X2 = 110

By using the slope formula we can obtain the value of P

m = Y1 - Y2 / X1 -X2

m = 330-0/0-110

m = 330/-110

m = -3

To obtain the value of y

Y - Y1 = P (X - x1) Start with the point-slope form.

Substitute the slope for m and (330, 0) for the x and y.

Use distributive property and then add 330 to both sides.

Multiply both sides by 3.

Add 3x to both sides and change to less than or equal to symbol.

Y - 330 = -3 (X - 0)

Y = -3x + 330

Multiply and divide y on both sides

-3x / -3 = y/-3-330/-3 (where y = 330)

-3y = 1x + 110

-3y + 1x < 110

Refrigerators = y = 71

Televisions = x = 118

Putting the value of x and y in the above equation that has obtain in first part

-3(71) + (118) < 110

- 213 + 118 < 110

-95 < 110 This is a true statement, so the television values is higher than Refrigerators.

The value is negative; it means that no truck has interested to hold 118 Television and 71 Refrigerators.

Refrigerators = y = 51

Televisions = x = 176

Putting the value of x and y in the above equation that has obtain in first part

-3(51) + (176) < 110

-153 + 176 < 110

23 < 110 This is a false statement so the TV and Refrigerator will not hold the amount given.

The value is positive; it means that the truck has interested to hold 176 Television and 51 Refrigerators.

Question # 69

The diagram is showing the total number of Television on the y axis and number of refrigerators on x axis. There are two points has noticed in this graph such as (0,330) and (110, 0), so we can make a slope by using these two points.

The formula of slope is defines as

m = 330-0/0-110

m = -3

The point-slope form of a linear equation to write the equation itself can now be used. These are the steps we take to arrive at our linear inequality.

y - y1 = m(x - x1)

y - 330 = (-3) (x-0)

y = -3x +330

3y = -x + 110

-x + 3y = 110

The graph has a solid line or dashed line rather than a dotted line indicating that points on the line itself are part of the ...