Solve for the point of intersection in the following system of equations and show your work using the substitution and elimination methods: y=x-2 3x-y=16

Answer 1

Using Substitution:

y = x - 2

3x - y = 16

Since y = x - 2, we can substitute "x - 2" into the second equation wherever there is a "y" so the second equation becomes:

3x -(x - 2) = 16

Distributing the "-" to the two elements inside the parenthesis gives us:

3x - x + 2 = 16 or

2x + 2 = 16 then subtract 2 from both sides to get:

2x = 14 then divide both sides by 2 to get:

x = 7 then plug 7 in for x in the original equation to get y = 7 - 2 or y = 5

The solution (point of intersection) then is the point (7, 5)

Using Elimination:

y = x - 2

3x - y = 16

Re-write the first equation in the for (Ax + By = C) by subtracting "y" from both sides and adding 2 tho both sides to get: x - y = 2. Recognize that to eliminate a variable, the easiest would be "y" but I need to multiply the first equation by "-1" to get a +y on the first equation that will add to a "-y" in the second equation to eliminate the y variable. So, multiplying the new first equation by -1 we get:

-x + y = -2 Now write the second equation below this:

3x - y = 16 add these two equations together:

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2x = 14 Now divide both sides by 2 to get:

x = 7 Now plug this into the original equation to get y = 5

The solution then is the point (7, 5)

Answer 2

Using substitution, we can substitute for y in the 2nd equation (x-2). Thus 3x - (x-2) = 16 ----->3x - x + 2 = 16

---------> 2x + 2 = 16 --------> 2x = 14 --------> x = 7 and since y = x - 2 = 7 - 2 = 5

So our solution is the point (7,5)