Question

A pair of equations is shown below: y = 7x - 8 y = 5x - 2 Part A: Explain how you will solve the pair of equations by substitution or elimination. Show all the steps and write the solution (5 points) Part B: If the two equations are graphed, at what point will the lines representing the two equations intersect? Explain your answer. (5 points)

Answer 1

So, first of all you have to identify the two equations which are: y=7x-8 and y=5x-2. after identifying the two equation you can choose one of them to start with. I chose the first one and I'll use substitution method, which means I'll pug in numbers in the unknown variables to find the value of x. Y=7x-8, I'll substitute the value of y in the equation that I chose and plug in the value of the second equation. Y=7x-8 --> 5x-2=7x-8 (this is our new equation). After that I'll combine like terms. -2+8=7x-5x --> 6=2x  --> 6/2=x --> 3=x. So x=3 and that's the answer using substitution method. If the two points are graphed, they will intersect at the point (3,13). To see where the intersection of the line we can use a calculator to make it faster. So we plug in the points of the two lines in the calculator we graph and find the intersection point.