Final answer:
The question involves solving a system of two linear equations using algebraic methods or graphing. The equations form lines on a graph, and the point of intersection is the solution.
Step-by-step explanation:
The question refers to solving a system of linear equations 2x-3y=8 and -3x+2y=8. To solve this system, we can use either the substitution method, the elimination method, or graphing. For example, using the elimination method, multiply the first equation by 2 and the second equation by 3 to make the coefficients of x to be equal but with opposite signs. The modified equations would be 4x - 6y = 16 and -9x + 6y = 24. Then, by adding these equations, we can eliminate y and find the value of x. Afterwards, we substitute the value of x into one of the original equations to find the value of y, giving us the solution to the system.
If plotting these equations on a graph, they represent two lines. The point where they intersect is the solution to the system. Additionally, the slope-intercept form, such as y = 9 + 3x, represents a straight line where 9 is the y-intercept and 3 is the slope (rise over run). To graph this line, you start at the y-intercept (0, 9) and use the slope to find other points. Plot these points and draw a line through them for the visual representation of the equation on a graph.