Solving Linear Systems: When Does z ≠ 1? | ACT Math Short

???? Description:
Ready to solve linear systems? Let’s figure out which value of z will make the system have no solutions!

Problem:
Which of the following values of z will make the system have no solutions?
x + y = 1
x + y = z

Options:
A) z ≠ 1
B) z = 1
C) z ≠ 0
D) z = 0

Quick Breakdown:
1️⃣ Identify the system:
The system is made up of two equations where x + y appears on both sides.

x + y = 1
x + y = z
2️⃣ Substitute and simplify:
By substituting x + y = 1 into the second equation, we get:

z = 1
This means for the system to have a solution, z must equal 1.
3️⃣ Answer:
For the system to have no solutions, z cannot equal 1. If z ≠ 1, the two equations are inconsistent and there is no solution.

The correct answer is Option A: z ≠ 1!

???? Key Takeaways:

A system has no solutions when the lines are parallel with the same slope but different y-intercepts.
To make the system inconsistent, z must not equal 1.
???? Got questions or thoughts? Drop them in the comments and don’t forget to like & subscribe for more SAT Math tips! ????

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