1. Problem: Solve the simultaneous linear equations $2x + y = 8$ and $x + y = 5$ by graphing. 2. Step 1: Identify the system type. These are simultaneous linear equations because there are two linear equations with two variables. 3. Step 2: Express each equation in slope-intercept form $y = mx + b$ for graphing. For $2x + y = 8$, subtract $2x$ from both sides: $$y = 8 - 2x$$ For $x + y = 5$, subtract $x$ from both sides: $$y = 5 - x$$ 4. Step 3: Graph both lines on the coordinate plane. The lines are straight because these are first degree equations. 5. Step 4: Find the point of intersection of the lines which satisfy both equations. Set the right hand sides equal: $$8 - 2x = 5 - x$$ Simplify: $$8 - 2x = 5 - x$$ $$8 - 5 = -x + 2x$$ $$3 = x$$ 6. Step 5: Substitute $x=3$ into one equation to find $y$. Using $y = 5 - x$: $$y = 5 - 3 = 2$$ 7. Final Answer: The solution to the system is $$x = 3, y = 2$$ This means the lines intersect at the point $(3,2)$, solving the simultaneous equations.