Question 127985
1a.The sales representative informs you that there are two floor plans still available, and that there are a total of 56 houses available. Use x to represent floor plan #1 and y to represent floor plan #2. Write an equation that illustrates the situation. 

{{{x + y = 56 }}}……………(a)

1b. The sales representative later indicates that there are 3 times as many homes available with the second floor plan than the first. Write an equation that illustrates this situation. Use the same variables you used in part a.

{{{ y=3x }}}…………(b)

1c. Use the equations from part a and b of this exercise as a system of equations. Use substitution to determine how many of each type of floor plan is available. Describe the steps used to solve the problem.

{{{x + y = 56 }}}……………(a)
{{{ y=3x   }}}…………(b)….substitute {{{y}}}from this equation from (a)
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{{{x + y = 56 }}}……………(a)
{{{ x+ 3x = 56}}}
{{{ 4x = 56}}}
{{{ x = 56/4}}}
{{{ x = 14}}}

{{{ y=3x   }}}…………(b)….
{{{ y=3*14  }}}
{{{ y=42  }}}


1d. What are the intercepts of the equation from part a of this problem? What are the intercepts from part b of this problem? Where would the lines intersect if you solved the systems by graphing?
the intercepts are:

{{{x + y = 56 }}}……………(a)…if {{{x=0}}}, {{{y-intercept}}} will be:

{{{0+y=56}}}
{{{y=56}}}……………………… so, {{{y-intercept}}} is ({{{0}}},{{{56}}})

if {{{y=0}}}, {{{x-intercept}}} will be:

{{{x+0=56}}}
{{{x=56}}}…………….so, {{{x-intercept}}} is ({{{56}}},{{{0}}})


*[invoke graphing_linear_equations "standard", 1, 1, 56, 2, 1]