Write an equation that gives the cost C of driving the car x

Write an equation that gives the cost C of driving the car x miles. Use the intersection-of-graphs method to deter­mine the number of miles that the car is driven if the rental cost is $90. Solve part (b) numerically with a table of values. Supplementary Angles The smaller of two supple­mentary angles is 30 Degree less than the measure of the larger angle. Find each angle. Triangle In an isosceles triangle, the measures of the two smaller angles arc equal and their sum is 40 Degree more than the larger angle. Let x be the measure of each of the two smaller angles and y be the measure of the larger angle. Write a system of linear equations whose solu­tion gives the measures of these angles. Use the method of substitution to solve the system. Use the method of elimination to solve the system. Garden Dimensions A rectangular garden has 88 feet of fencing around it. The garden is 4 feet longer than it is wide. Find the dimensions of the garden. Room Prices Ten rooms are rented at rates of $80 and $120 per night. The total collected for the 10 rooms is $920. Write a system of linear equations whose solution

Solution

71. (a) x+x = 40+y => 2x= 40+y => 2x-y= 40

And also x+x+y = 180 (angle sum property of a triangle

=> 2x+y = 180

Hence the system of linear equations is given by:

2x-y = 40

2x+y = 180

(b) From first equation, we get 2x-40 = y

Substitute this y in second equation, we get:

2x+2x-40 = 180

=> 4x-40 = 180

=> 4x = 220 => x = 55

y = 2(55)-40 = 70

Hence x = 55, y = 70

(c) Add two equations to eliminate y , we get:

4x = 220 => x = 55

Again 2(55)-y = 40 => 110 -40 = y => y =70

So, x=55, y= 70