Question

Graph the system of equations below on a piece of paper. What is the solution?
y= 2x - 3
y= -x+3
• A. (1.-1)
B. (3,0)
CC. (2.1)
D. (0, -3)

Answer 1

To find the solution to the system of equations given, you'll want to graph the two lines defined by the equations:

1. \( y = 2x - 3 \)
2. \( y = -x + 3 \)

Let's analyze each equation:

1. **For the first equation** \( y = 2x - 3 \):
- When \( x = 0 \), \( y = -3 \) (the y-intercept).
- When \( x = 1 \), \( y = 2(1) - 3 = -1 \).
- When \( x = 2 \), \( y = 2(2) - 3 = 1 \).
- When \( x = 3 \), \( y = 2(3) - 3 = 3 \).

So, some points for this line are: \( (0, -3) \), \( (1, -1) \), \( (2, 1) \), \( (3, 3) \).

2. **For the second equation** \( y = -x + 3 \):
- When \( x = 0 \), \( y = 3 \) (the y-intercept).
- When \( x = 1 \), \( y = -1 + 3 = 2 \).
- When \( x = 2 \), \( y = -2 + 3 = 1 \).
- When \( x = 3 \), \( y = -3 + 3 = 0 \).

Some points for this line are: \( (0, 3) \), \( (1, 2) \), \( (2, 1) \), \( (3, 0) \).

### Finding the Intersection

To find the solution to the system of equations, you need to find where the two lines intersect.

Set the equations equal to each other:
\[ 2x - 3 = -x + 3 \]

Now solve for \( x \):
\[ 2x + x = 3 + 3 \]
\[ 3x = 6 \]
\[ x = 2 \]

Now substitute \( x = 2 \) back into either equation to find \( y \):
Using \( y = 2x - 3 \):
\[ y = 2(2) - 3 = 4 - 3 = 1 \]

So, the intersection point (solution) is \( (2, 1) \).

### Conclusion

Thus, the solution to the system of equations is \( (2, 1) \), which corresponds to option **C. (2, 1)**.