Question

$y = x - 3$
$y = -x + 5$
which describes the system of equations above?
consistent and dependent
consistent and independent
inconsistent

Explanation:

Step1: Identify slope-intercept form

The equations are in $y=mx+b$ form, where $m$ is slope, $b$ is y-intercept.
For $y=x-3$: $m_1=1$, $b_1=-3$
For $y=-x+5$: $m_2=-1$, $b_2=5$

Step2: Analyze system consistency

Consistent systems have at least one solution. Independent systems have distinct, non-parallel lines (different slopes). Since $m_1
eq m_2$, lines intersect at one point.

Step3: Classify the system

A system with exactly one solution is consistent and independent.

Answer:

consistent and independent