To solve the system of equations graphically, we need to plot both equations on the coordinate plane and find the point where they intersect.

The system of equations is:

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

Step 1: Rearrange the equations to slope-intercept form (i.e., $y = mx + b$).

• For the first equation: $x + y = 7$ $y = -x + 7$ This is a straight line with slope $-1$ and y-intercept $7$.

• For the second equation: $x - y = 3$ $y = x - 3$ This is a straight line with slope $1$ and y-intercept $-3$.

Step 2: Plot the lines

• The first line $y = -x + 7$ has a negative slope and crosses the y-axis at $7$.
• The second line $y = x - 3$ has a positive slope and crosses the y-axis at $-3$.

Step 3: Find the intersection point

The intersection of these two lines will give the solution to the system.

To solve algebraically, set the two equations equal to each other: $-x + 7 = x - 3$ Solving for $x$: $7 + 3 = 2x \quad \Rightarrow \quad 10 = 2x \quad \Rightarrow \quad x = 5$ Now, substitute $x = 5$ into either equation to find $y$: $5 + y = 7 \quad \Rightarrow \quad y = 2$

Thus, the solution is $(5, 2)$.

Would you like me to provide a detailed graphical plot for this system, or do you have any questions?

Related Questions:

1. What is the slope of the line $x + y = 7$?
2. How can we interpret the intersection point of two lines graphically?
3. What happens when two lines are parallel in a system of linear equations?
4. Can we solve this system using substitution or elimination methods?
5. How do you determine the slope from a linear equation?

Tip:

Always check your graphical solution by substituting the coordinates of the intersection back into both original equations to ensure accuracy.