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Big Ideas Math Algebra 1, 2015
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Big Ideas Math Algebra 1, 2015 View details
Cumulative Assessment
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Exercise 3 Page 352

Practice makes perfect
a We are asked to select two equations which form a system of equations that has infinitely many solutions.
  • For a system to have infinitely many solutions, it must mean that the lines intersect at infinitely many points. Such lines are said to be coincidental, and they have the same slope and y-intercept.First, we will rewrite each equation in slope-intercept form and find the slope and the y-intercept for each equation. Let's do it for 3x+y=12!
    3x+y=12
    SubEqn

    LHS-3x=RHS-3x

    y=- 3x+12
    Therefore, the slope is equal -3 and the y-intercept is 12. Let's do this for the remainder of the given equations, too.
    Equation Slope-Intercept Form Slope y-intercept
    3x+y=12 y= - 3x+ 12 - 3 12
    3x+2y=12 y= -3/2x+ 6 -3/2 6
    6x+2y=6 y= - 3x+ 3 - 3 3
    3y+9x=36 y= - 3x+ 12 - 3 12
    2y-6x=12 y= 3x+ 6 3 6
    9x-3y=- 18 y= 3x+ 6 3 6

    From the table we can see that 3x+y=12 and 3y+9x=36 have the same slope and y-intercept. Therefore, the following system of equations has infinitely many solutions. 3x+y=12 3y+9x=36

b We are asked to select two equations which form a system of equations that has exactly one solution.
  • For a system to have only one solution, it must mean that the lines intersect at only one point. Such lines must have unequal slopes.

From the table in Part A we can see that the equations 3x+y=12 and 3x+2y=12 have different slopes. Therefore, the following system of equations has one solution. 3x+y=12 3x+2y=12

c We are asked to select two equations which form a system of equations with no solution.
  • For a system to have no solution, it must mean that the lines do not intersect. Such lines must be parallel, meaning that they have the same slope and different y-intercepts.

From the table from Part A we can notice that the equations 3x+y=12 and 6x+2y=6 have the same slope but different y-intercepts. Therefore, the following system of equations has no solutions. 3x+y=12 6x+2y=6

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