To solve the system of equations by finding the point where the lines intersect, we have:

$y = -2x + 3$ $y = 3x - 7$

Since both equations are equal to $y$, we can set them equal to each other to solve for $x$:

$-2x + 3 = 3x - 7$

Now, solve for $x$:

1. Add $2x$ to both sides: $3 = 5x - 7$

2. Add $7$ to both sides: $10 = 5x$

3. Divide by $5$: $x = 2$

Now, substitute $x = 2$ back into one of the original equations to find $y$. Using $y = -2x + 3$:

$y = -2(2) + 3$ $y = -4 + 3$ $y = -1$

Thus, the solution to the system is the point $(2, -1)$.

Answer

The solution to the system is: $(x, y) = (2, -1)$

Would you like more details on the method or any further questions?

1. How do we interpret solutions of systems on graphs?
2. Why do we set equations equal to solve systems algebraically?
3. What are methods to solve systems if no graphs are given?
4. How can systems with parallel lines be identified?
5. What is the significance of a solution to a system in real-world applications?

Tip: When graphing, always check for slopes and intercepts first; they provide clues to intersection points.