Let me help you solve the systems of equations shown in the image.

System A:

The system of equations is:

1. $x + 3y = 9$
2. $-x - 3y = -9$

Let's add these two equations to eliminate $x$:

$(x + 3y) + (-x - 3y) = 9 + (-9)$

$0 = 0$

Since both variables cancel out and we are left with a true statement, this indicates that System A has infinitely many solutions. The equations represent the same line. Therefore, all solutions satisfy the same line's equation, which is:

$y = \frac{9 - x}{3}$

System B:

The system of equations is:

1. $x + 4y = 8$
2. $-x - 4y = 8$

Let's add these two equations to eliminate $x$:

$(x + 4y) + (-x - 4y) = 8 + 8$

$0 = 16$

Since we are left with a contradiction (0 does not equal 16), this indicates that System B has no solution. The two lines are parallel and never intersect.

Would you like further details or have any questions?

5 Related Questions:

1. How do we determine if a system has infinitely many solutions?
2. What are the steps to solve a system of linear equations using substitution?
3. How can we recognize if two lines are parallel or the same line?
4. What does it mean when a system of equations is inconsistent?
5. How do you find the equation of a line given two points?

Tip:

When solving a system of equations, always check if adding or subtracting the equations can eliminate one variable to simplify the system.