Solve the following system of equations by graphing: x + 2y = 8 x - y = 2

Steps to Solve

1. Solve each equation for $y$ Isolate $y$ in each equation to express them in slope-intercept form ($y = mx + b$). For the first equation: $x + 2y = 8$ $2y = -x + 8$ $y = -\frac{1}{2}x + 4$ For the second equation: $x - y = 2$ $-y = -x + 2$ $y = x - 2$

2. Find two points for each line Choose two $x$ values and calculate the corresponding $y$ values for each equation: For $y = -\frac{1}{2}x + 4$: If $x = 0$, $y = -\frac{1}{2}(0) + 4 = 4$. Point: $(0, 4)$ If $x = 2$, $y = -\frac{1}{2}(2) + 4 = -1 + 4 = 3$. Point: $(2, 3)$

   For $y = x - 2$: If $x = 0$, $y = 0 - 2 = -2$. Point: $(0, -2)$ If $x = 2$, $y = 2 - 2 = 0$. Point: $(2, 0)$

3. Plot the points and draw the lines Plot the points found in step 2 on a coordinate plane and draw a straight line through the points for each equation.

4. Find the intersection point Identify the point where the two lines intersect on the graph. This point represents the solution to the system of equations. From the graph, the intersection point appears to be $(4, 2)$.

5. Verify the solution Substitute the $x$ and $y$ values of the intersection point into both original equations to check if the solution is correct. For $x + 2y = 8$: $4 + 2(2) = 4 + 4 = 8$. The equation holds true. For $x - y = 2$: $4 - 2 = 2$. The equation holds true.