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Intercepts, substitutions and graphs

1. y = 2x + 3 and y = -x - 4

2. 2x + 3y = 8 and 3x + 2y = 7

3. x + y = 3 and y = x + 3

4. A university bookstore recently sold a wirebound graph-paper notebook for $2.50, and a college-ruled notebook for $2.30. At the start of spring semester, a combination of 50 of these notebooks were sold for a total of $118.60. How many of each type were sold?

5. A shopper buys three oranges and five lemons for $10.26, while a second shopper buys four lemons and six oranges for $11.16. What is the price of each fruit?

6. In a triangle, the sum of the interior angles is 180 degrees. If angle A is three times as large as angle B, and angles B and C sum to 90 degrees, what is the measure of each angle?

7. The sum of two numbers is 72. One of the numbers is six more than twice the other. What are the two numbers?

8. A bricklayer and an electrician together spend 90 hours working on a new house. If the bricklayer earns $12 per hour, the electrician earns $16 an hour, and the owner pays them a total of $1350 for their work, how many hours does each worker spend on the house?

Solution Preview

1. y = 2x + 3 and y = -x - 4

Y=2x+3, set x=0, y=3; (0,3)
Set y=0;x=-3/2; (-3/2,0)

Graph in attachment

Y=-x-4, set x=0; (0,-4)
Set y=0; (4,0)

Graph in attachment

2. 2x + 3y = 8 and 3x + 2y = 7

2x+3y=8; set x=0; y=8/3; (0,8/3)
Set y=0; (4,0)

Repeat for 3x+2y=7; 3(1)+2(2)=7; 7=7
set x=0; y=7/2 (0,7/2)
set y=0;x=7/3 (7/3,0)

Graph in attachment

3. x + y = 3 and y = x + 3

Sub x+x+3=3; 2x=0;x=0; y=3
Graph
Set x=0; (0,3)
Set y=0; (3,0)

Graph in attachment

4. A university bookstore recently sold a wirebound graph-paper notebook for $2.50, and a college-ruled notebook for $2.30. At the start of spring semester, a combination of 50 of these notebooks were sold ...

Solution Summary

This solution demonstrates finding x-intercepts and y-intercepts and finding solutions by adding equations and substituting values. Graphs are included in the attachment.

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