Question

what result indicates no solution when using elimination?
a. the equation simplifies to a false statement like $0=3$
b. the equation reduces to a tautology like $0=0$
c. the variables are not eliminated
d. the variables all cancel out to 0

if solving for $x$ and $y$ in a system, and you substitute $x=3$ into $y=2x+1$, what is $y?$
a. 5
b. 4
c. 7
d. 6

Explanation:

Step1: Identify no solution indicator

For elimination method, a false statement (e.g., $0=3$) means no solution.

Step2: Substitute $x=3$ into equation

Substitute $x=3$ into $y=2x+1$:
$y=2(3)+1$

Step3: Calculate value of $y$

$y=6+1=7$

Answer:

1. a. The equation simplifies to a false statement like 0 = 3
2. c. 7