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4 years ago

PLEASE HELP!

1 answer:

6 0

There are various ways to solve this. I will solve by elimination which seems easier:
I multiply the top equation by 1/2 to get 1/4y so I can eliminate y:
-3x/8 + 1y/4 = -1 Now add the second equation:
1x/5 - 1y/4 = -6 This gives:
------------------------------------
-3x/8 + 1x/5 = -7 Get a common denominator:
-15x/40 + 8x/40 = -7 Now add fractions:
-7x/40 = -7 Multiply by the reciprocal(-40/7):
x = 7 × 40 / 7 Simplify:
x = 40.
Now plug in 40 for x in one of the equations and solve for y (2nd equation looks easier):
1(40)/5 - 1y/4 = -6
8 - y/4 = -6 subtract 8
-y/4 = -14 multiply by 4
-y = -56
y = 56.

So we got x=40 and y=(56) new lets check!
-3(40)/4 + (56)/2 = -2
-3(10) + 28 = -2
-30 + 28 = -2
-2 = -2.

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$\begin{gathered} E=x_1+vt----1 \\ E=x_2+vt----2 \\ where\colon E=elevation,ft;x=InitialElevation,ft; \\ v=velocity,ft\text{/}min;t=time,min \\ x_1=80,870ft,v=-450ft\text{/}min \\ E=80870-450t----1 \\ x_2=5,000ft,v=900ft\text{/}min \\ E=5000+900t----2 \end{gathered}$

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$\begin{gathered} 5000+900t=80870-450t \\ \text{Add 450t to both sides, we have:} \\ 900t+450t+5000=80870-450t+450t \\ 1350t+5000=80870 \\ \text{Subtract 5000 from both sides, we have:} \\ 1350t+5000-5000=80870-5000 \\ 1350t=75870 \\ \text{Divide both sides by 1350, we have:} \\ \frac{1350t}{1350}=\frac{75870}{1350} \\ t=56.2min \\ \\ \text{After }56.2\text{ minutes, both airplanes will be at the same elevation} \end{gathered}$

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$\begin{gathered} E_1=80870-450t \\ E_1=80870-450(56.2) \\ E_1=80870-25290 \\ E_1=55580ft \\ \\ E_2=5000+900t \\ E_2=5000+900(56.2) \\ E_2=5000+50580 \\ E_2=55580ft \\ \\ \therefore E_1\equiv E_2=55580ft \end{gathered}$

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