Correct answer: A

The correct answer is $(x,y)=(6,4)$.

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: Add the equations to get $2x=12$, so $x=6$. Substitution gives $y=4$.
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 $(x,y)=(4,3)$.

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: Subtract the second equation from the first: $x=4$. Then $4+y=7$, so $y=3$.
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 $(x,y)=(4,2)$.

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: From the second equation, $x=y+2$. Substitute to get $y+2+2y=8$, so $y=2$ and $x=4$.
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 $(x,y)=(2,4)$.

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: Subtract the second equation from the first: $2x=4$, so $x=2$. Then $y=4$.
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 $(3,5)$.

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 system directly gives the ordered pair $(x,y)=(3,5)$.
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 $(x,y)=(2,5)$.

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 for $y$ equal: $2x+1=-x+7$. Thus $3x=6$, $x=2$, and $y=5$.
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 $(x,y)=(3,2)$.

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: Multiply the second equation by 2: $2x+2y=10$. Subtract to get $y=2$, then $x=3$.
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 $(x,y)=(3,3)$.

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: Add the equations to get $5x=15$, so $x=3$. Then $y=3$.
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 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: The second equation is twice the first, 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.

Correct answer: B

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: Multiplying the first equation by 2 gives $2x+2y=8$, which conflicts with $2x+2y=10$.
3. Check both equations: Substitute the ordered pair into both original equations and verify that it satisfies each one.