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andrey2020 [161]
3 years ago
10

Find the ordered pair (s, t) that satisfies the system

Mathematics
1 answer:
sertanlavr [38]3 years ago
4 0

\left\{\begin{array}{ccc}\dfrac{s}{2}-3t=-1&\text{multiply both sides by 4}\\3t-2s=3\end{array}\right\\\underline{+\left\{\begin{array}{ccc}2s-12t=-4\\3t-2s=3\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad -9t=-1\qquad\text{divide both sides by (-9)}\\.\qqud\qquad\boxed{t=\dfrac{1}{9}}\\\\\text{Put the value of t to the second equation}\\\\3\left(\dfrac{1}{9}\right)-2s=3\\\\\dfrac{1}{3}-2s=3\qquad\text{subtract}\ \dfrac{1}{3}\ \text{from both sides}

-2s=2\dfrac{2}{3}\qquad\text{divide both sides by (-2)}\\\\s=\dfrac{8}{3}\cdot\left(-\dfrac{1}{2}\right)\\\\\boxed{s=-\dfrac{4}{3}}\\\\Answer:\ \boxed{\left(-\dfrac{4}{3},\ \dfrac{1}{9}\right)}

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Answer:

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Step-by-step explanation:

The easiest way of find the answer for this is to use what is called the "point-slope" form of a line, because you are in fact given the value of the slope (m) and also a point   (x_0,y_0)  it goes through:

y-y_0=m\,(x-x_0)

In our case the equation becomes:

y-y_0=m\,(x-x_0)\\y-6=2\,(x-4)\\

This can also be written in the slope-intercept form by solving for "y" and operating to remove the parenthesis:

y-6=2\,(x-4)\\y=2x-8+6\\y=2x-2

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