Imagine you are in the market for a new home and are interested in a new housing community under construction in a different city

a. We know that there are exactly 56 houses and each house has one of the two floor plans, so x + y = 56

b. As stated simply, y = 3x : if you multiply the number of houses with floor plan 1 by 3, you get the number of houses with floor plan 2.

c. Our equations are x+y=56 and y=3x. Substituting y from the second equation (3x in other words) into the first equation, we get x + 3x = 56. Combining like terms: 4x = 56. Solving for x: x = 14. There are three times as many y's as there x's, so y = 3x = 3*14 = 42. You can verify that these answers satisfy both equations simultaneously.

d. The first equation was x + y = 56. The intercepts occur where either x or y is zero. Making x zero, y= 56. Making y zero, x = 56. So the intercepts are at (56, 0) and (0, 56). The second equation was 3x = y. Making x zero, y = 0. Making y zero, x = 0. So it crosses the origin (0, 0). The lines would intersect at the point that satisfies both equations, which have figured out is (14, 42).