Three students are working to find the solution set of this system of equations:
y = 3x – 4
2y = 6x – 8
Use the drop-down menus to complete the statements about each of their methods.
Dominick
Dominick correctly graphs the two lines and sees that they _______ solution(s). This means the system has _______.
Susie
Susie correctly sees that 2y = 6x – 8 _______ a multiple of y = 3x – 4.
John
John correctly concludes that because dividing 2y = 6x – 8 by 2 will _______ be equal to y = 3x – 4, the system has _______ solution(s).
Let’s go through each student’s methods to help you find the right answers.
Dominick:
Dominick correctly graphs the two lines and sees that they have one solution(s). This means the system has intersecting lines. This indicates that the lines meet at one point, which is the solution to the system.
Susie:
Susie correctly sees that 2y = 6x – 8 is a multiple of y = 3x – 4. This means that the two equations represent the same line.
John:
John correctly concludes that because dividing 2y = 6x – 8 by 2 will result in y = 3x – 4, the system has infinitely many solution(s). This means that since both equations are the same, they overlap completely, providing an infinite number of points that satisfy both equations.
So, in summary:
– Dominick: a) one; b) intersecting lines.
– Susie: is.
– John: will; infinitely many.
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