Use Substitution And Elimination Method

Substitution: y=x2-6x+9                      y+x=5     Elimination: y=x2-11x-36                   y=-12x+36

Solution


Greetings! Lets solve this shall we ?

So, after reviewing this problem I see we cannot use elimination for the second part. We must use substitution for both problems such that

y + x = 5 and y = x2 – 6x + 9 where

y = -x + 5 and y = x2 – 6x + 9 such that

-x + 5 = x2 – 6x + 9………………Now we solve for x first by adding x to both sides such that

5 = x2 – 5x + 9………………Then subtracting 5 to both sides to get

0 = x2 – 5x + 4……………..We can factor this into

0 = (x-1)(x-4)……………….Then use the Zero-Product Property of Equality such that

x – 1 = 0 and x – 4 = 0………………Then the x-values are

x = 1 and 4

Now we plug these values into the equation such that

y = -(1) + 5

y = 4

and

y = -(4) + 5

y = 1

So, the solutions are (1,4) and (4,1) for the first system of equations.

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Then, we must solve the second system of equations such that elimination will not work due to it having an x squared term. So, we must use substitution method. Then,

-12x + 36 = x2 – 11x – 36……………..First we add 12x to both sides such that

36 = x2 + x – 36………………Then we subtract 36 to both sides such that

0 = x2 + x – 72……………….We see this polynomial is factorable so we find factors that will add to give us

0 = (x+9)(x-8)…………….Then

x = -9,8

So, we plug these values into the equation y = -12x + 36 to get the solutions (-9,144) and (8, -60).

I hope this helped!