Question

Elsa and Olaf's teacher gave them a system of linear equations to solve. They

each took a few steps that led to the systems shown in the table below.
1, Systems
quivalent
tions and the
hod
Teacher
5x + 3y = -1
stems of
with elimination
43 - 9y = 8
Elsa
method
tems of linear
4.2 - 9y = 8
Olaf
15x + 9y = -3
4x - 9y = -5
9x - y = 7
cample:
systems of
Which of them obtained a system that is equivalent to the teacher's system?
Remember that two linear systems are "equivalent" if they have the same solution.
kample: non-
systems of
Choose 1 answer:
t systems of
review
~
Only Elsa
® Only Olaf
lutions to sys...
Both Elsa and Olaf

Answer 1

(a) Only Elsa

Explanation:

Both Elsa and Olaf made mistakes in their solution of the system of equations. However, the mistake Elsa made does not change the solution to the system of equations.

Elsa's work

Apparently, Elsa's first equation is identical to the Teacher's second equation. Elsa's second equation is the sum of the Teacher's two equations. This system will have the same solution as the Teacher's system of equations, so Elsa's result is an equivalent system.

Olaf's work

Olaf's first equation is the Teacher's first equation, multiplied by 3. Olaf's second equation is the Teacher's second equation with the constant changed from 8 to -5. That gives a line parallel to the line described by the Teacher's second equation, so will have a different intersection point with the first equation. Olaf's result is not an equivalent system.

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Additional comment

Olaf successfully set up the equations so the y-coefficients are opposite and will cancel when his two equations are added. However, the mistake of changing the constant in the second equation means his result will be in error.

The operation Elsa performed is a legitimate operation on the system of equations, but it gets her no closer to a solution.