A set of equations is given below:
2 answers:
Answer:
C.
Step-by-step explanation:
We have been given a set of equations as:
Equation A:
Equation B:
We can see that the given set of equations represent system of linear equation.
We will use substitution property of equality, which states when , then x can be substituted in any equation in place of y and y can be substituted in place of x in any equation as well.
To solve our given system of equations we need to equate our given equations as:
Therefore, option C is the correct choice.
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Start with the answer format we want, and work your way toward forming a single fraction like so
Compare that last expression to (2x+1)/(x+2). Notice how the ax and 2x match up, so a = 2 must be the case.
Then we have 2a+b as the remaining portion in the numerator. Plugging in a = 2 leads to 2a+b = 2*2+b = 4+b. Set this equal to the +1 found in (2x+1)/(x+2) to have the terms match.
So, 4+b = 1 leads to b = -3
Therefore, a = 2 and b = -3
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An alternative route:
I added and subtracted 4 in the third step so that I could form 2x+4, which then factors to 2(x+2). That way I could cancel out a pair of (x+2) terms toward the very end.
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Other alternative methods involve synthetic division or polynomial long division. They are slightly separate but related concepts.