Correct answer: A

The correct answer is The ordered pair that satisfies both equations.

1. Choose a system method: Use substitution, elimination, a graph, or an equivalent form that makes one variable easy to determine.
2. Solve for the ordered pair: A graph intersection has coordinates that lie on both lines, so the ordered pair is the system solution.
3. Check both equations: Substitute the ordered pair into both original equations and verify that it satisfies each one.

Correct answer: B

The correct answer is $(x,y)=(4,4)$.

1. Choose a system method: Use substitution, elimination, a graph, or an equivalent form that makes one variable easy to determine.
2. Solve for the ordered pair: Set the equations equal: $0.5x+2=-x+8$. Thus $1.5x=6$, $x=4$, and $y=4$.
3. Check both equations: Substitute the ordered pair into both original equations and verify that it satisfies each one.

Correct answer: C

The correct answer is No solution.

1. Choose a system method: Use substitution, elimination, a graph, or an equivalent form that makes one variable easy to determine.
2. Solve for the ordered pair: Parallel lines have the same slope and different intercepts, so they never intersect.
3. Check both equations: Substitute the ordered pair into both original equations and verify that it satisfies each one.

Correct answer: D

The correct answer is Infinitely many solutions.

1. Choose a system method: Use substitution, elimination, a graph, or an equivalent form that makes one variable easy to determine.
2. Solve for the ordered pair: Every point on the shared line satisfies both equations, so the system has infinitely many solutions.
3. Check both equations: Substitute the ordered pair into both original equations and verify that it satisfies each one.

Correct answer: A

The correct answer is Its coordinates make both line equations true at the same time..

1. Choose a system method: Use substitution, elimination, a graph, or an equivalent form that makes one variable easy to determine.
2. Solve for the ordered pair: The shared point is exactly the ordered pair common to both graphs and both equations.
3. Check both equations: Substitute the ordered pair into both original equations and verify that it satisfies each one.

Correct answer: B

The correct answer is $(x,y)=(3,0)$.

1. Choose a system method: Use substitution, elimination, a graph, or an equivalent form that makes one variable easy to determine.
2. Solve for the ordered pair: Set the expressions equal: $x-3=3x-9$. Thus $x=3$ and $y=0$.
3. Check both equations: Substitute the ordered pair into both original equations and verify that it satisfies each one.

Correct answer: C

The correct answer is $(x,y)=(3,0)$.

1. Choose a system method: Use substitution, elimination, a graph, or an equivalent form that makes one variable easy to determine.
2. Solve for the ordered pair: Set equal: $-2x+6=x-3$. Thus $3x=9$, so $x=3$ and $y=0$.
3. Check both equations: Substitute the ordered pair into both original equations and verify that it satisfies each one.

Correct answer: D

The correct answer is $(x,y)=(-1,4)$.

1. Choose a system method: Use substitution, elimination, a graph, or an equivalent form that makes one variable easy to determine.
2. Solve for the ordered pair: Set equal: $2x+6=-x+3$. Thus $3x=-3$, so $x=-1$ and $y=4$.
3. Check both equations: Substitute the ordered pair into both original equations and verify that it satisfies each one.

Correct answer: A

The correct answer is A system with no solution.

1. Choose a system method: Use substitution, elimination, a graph, or an equivalent form that makes one variable easy to determine.
2. Solve for the ordered pair: The lines have the same slope 4 and different intercepts, so they are distinct parallel lines.
3. Check both equations: Substitute the ordered pair into both original equations and verify that it satisfies each one.

Correct answer: B

The correct answer is A system with infinitely many solutions.

1. Choose a system method: Use substitution, elimination, a graph, or an equivalent form that makes one variable easy to determine.
2. Solve for the ordered pair: Rearranging the first equation gives $y=-2x+6$, so both equations describe the same line.
3. Check both equations: Substitute the ordered pair into both original equations and verify that it satisfies each one.