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3 years ago

How can I do substitution method in Algebra 2? The equations are y= x^2-2x-3 and y=x^2+5x+11

1 answer:

7 0

$\bf \begin{cases} \boxed{y} = x^2-2x-3\\ y = x^2+5x+11 \end{cases}\qquad\qquad \stackrel{\textit{substituting on the 2nd equation}}{\boxed{x^2-2x-3} = x^2+5x+11} \\\\\\ ~~\begin{matrix} x^2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ -2x-3= ~~\begin{matrix} x^2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ +5x+11\implies -2x-3=5x+11\implies -3=7x+11 \\\\\\ -14=7x\implies \cfrac{-14}{7}=x\implies \blacktriangleright -2=x \blacktriangleleft$

$\bf \stackrel{\textit{since we know that }y = x^2-2x-3}{y=(-2)^2-2(-2)-3} \implies y = 4+4-3\implies \blacktriangleright y = 5 \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (-2,5)~\hfill$

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Answer: Our required formula becomes :

$a=f(b)=-13-\frac{7}{4}b$

Step-by-step explanation:

Since we have given that

$4a+7b=-52\\$

We need to write a formula for f(b) in terms of b So, it becomes

$4a=-52-7b\\\\a=\frac{-52-7b}{4}\\\\a=\frac{-52}{4}-\frac{7b}{4}\\\\a=-13-\frac{7b}{4}$

Hence, our required formula becomes :

$a=f(b)=-13-\frac{7}{4}b$

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Answer:

Step-by-step explanation:

Comment

The way the diagram looks when it is drawn is that you are going to need the sine function to solve for the side opposite which is CD.

Formula

Sin(A) = Sin(68 = opposite / hypotenuse Substitute values.

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sin(68) = altitude (side opposite) / 20 multiply both sides by 20

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