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# Algebra

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Find the ordered pair (s, t) that satisfies the system
(s/2) + 5t =3 - 7t + 8s
3t - 6s = 9 - 2t

Jun 15, 2024

#1
+1280
+1

First, let's put s in terms of t so we can do some subsitutions. We get

$$\quad s=-\frac{2\left(-4t+1\right)}{5}$$ from the first equation.

Subsituting this value of s into the second equation, we get

$$3t-6\left(-\frac{2\left(-4t+1\right)}{5}\right)=9-2t$$

Now, we solve for t. We get

$$\frac{-23t+12}{5}=9$$

$$-23t+12=45$$

$$t=-\frac{33}{23}$$

Now, we subsitute t back into the first equation to find s. We get

$$s=-\frac{62}{23}$$

We get $$s=-\frac{62}{23},\:t=-\frac{33}{23}$$

So our final answer is $$(-62/23, -33/23)$$

Thanks! :)

Jun 16, 2024

#1
+1280
+1

First, let's put s in terms of t so we can do some subsitutions. We get

$$\quad s=-\frac{2\left(-4t+1\right)}{5}$$ from the first equation.

Subsituting this value of s into the second equation, we get

$$3t-6\left(-\frac{2\left(-4t+1\right)}{5}\right)=9-2t$$

Now, we solve for t. We get

$$\frac{-23t+12}{5}=9$$

$$-23t+12=45$$

$$t=-\frac{33}{23}$$

Now, we subsitute t back into the first equation to find s. We get

$$s=-\frac{62}{23}$$

We get $$s=-\frac{62}{23},\:t=-\frac{33}{23}$$

So our final answer is $$(-62/23, -33/23)$$

Thanks! :)

NotThatSmart Jun 16, 2024