Nora and William are asked to solve the system of equations below without graphing. y-1 = 3
y=2x-
- 4x + 9
Nora wants to use substitution, inserting 2x - 4x + 9 in place of y in the upper equation and solving. William wants to rewrite y-1 = 3x as
y = 3x + 1 and begin by setting 3x + 1 equal to 2x - 4x + 9, and then solving. Which student is correct, and why?
2
O A. Neither student is correct. William is incorrect because, when substituting, the equation that gives the expression to substitute for ym
already have y isolated on one side. Nora is incorrect because the linear equation has to be substituted into the quadratic equation,
the other way around.
O B. Both students are correct because both methods reduce the system to a single quadratic equation that can be solved for X
O C. William is correct because his method reduces the system to a single quadratic equation that can be solved for x. Nora is incorrect
because the linear equation has to be substituted into the quadratic equation, not the other way around.
OD. Nora is correct because her method reduces the system to a single quadratic equation that can be solved for x. William is incorrect
because, when substituting, the equation that gives the expression to substitute for y must already have y isolated on one side.