Three students are working to find the solution set of this system of equations:
y = 2x – 5
3y = 6x – 15
Use the drop-down menus to complete the statements about each of their methods.
Josh
Josh correctly graphs the two lines and sees that they ________. This means the system has ________ solution(s).
Katie
Katie correctly sees that 3y = 6x – 15 ________ a multiple of y = 2x – 5.
Aki
Aki correctly concludes that because dividing 3y = 6x – 15 by 3 will ________ be equal to y = 2x – 5, the system has ________ solution(s).
Let’s break down each student’s method to find answers for the statements.
Josh:
Josh correctly graphs the two lines and sees that they overlap. This means the system has infinitely many solution(s).
*Explanation: Both equations represent the same line, so every point on that line is a solution.*
Katie:
Katie correctly sees that (3y = 6x – 15) is a multiple of (y = 2x – 5).
*Explanation: If you multiply the second equation (y = 2x – 5) by 3, you get (3y = 6x – 15).*
Aki:
Aki correctly concludes that because dividing (3y = 6x – 15) by 3 will result in (y = 2x – 5), the system has infinitely many solution(s).
*Explanation: This confirms that the two equations are equivalent, leading to an infinite number of solutions.*
So the completed statements are:
– Josh: overlap, infinitely many
– Katie: is
– Aki: result in, infinitely many