(08.03/08.05 mc) a pair of equations is shown below: y = 3x − 5 y = 6x − 8 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)

Part A:

So for this, I will be using substitution. Since y = 3x - 5 and y = 6x - 8, then 6x - 8 = 3x - 5 (If a = b and a = c, then b = c). Substitute 6x - 8 into the y of the first equation: . From here we can solve for x.

Firstly, subtract 3x on both sides:

Next, add 8 on both sides of the equation:

Next, divide both sides by 3 and your answer is x = 1.

Next, since we have the value of x, just substitute that in into either equation and solve for y.

To sum it up, x = 1 and y = -2.

Part B:

If the two equations were graphed, the lines would intersect at (1,-2). The solution of two lines is at the points where they intersect, and since we discovered algebraically that the solution was x = 1 and y = -2, they would intersect at (1,-2).

a.

step-by-step explanation:

step 1 distribute 2 to every term in the parentheses

step 2 add 10 on both sides of the equal sign

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