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nikdorinn [45]
3 years ago
8

What is the solution to the system of equations 1/4x+1 1/2y=5/8 3/4x-1 1/2y=3 3/8

Mathematics
1 answer:
AleksandrR [38]3 years ago
6 0

Answer:

\large\boxed{x=4,\ y=-\dfrac{1}{4}}

Step-by-step explanation:

\underline{+\left\{\begin{array}{ccc}\dfrac{1}{4}x+1\dfrac{1}{2}y=\dfrac{5}{8}\\\\\dfrac{3}{4}x-1\dfrac{1}{2}y=3\dfrac{3}{8}\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\dfrac{4}{4}x=3\dfrac{8}{8}\\\\.\qquad\boxed{x=4}\\\\\text{put the value of x to the first equation:}\\\\\dfrac{1}{4}(4)+1\dfrac{1}{2}y=\dfrac{5}{8}\\\\1+1\dfrac{1}{2}y=\dfrac{5}{8}\qquad\text{subtract}\ 1=\dfrac{8}{8}\ \text{from obth sides}\\\\1\dfrac{1}{2}y=-\dfrac{3}{8}\qquad\text{multiply both sides by 2}\\\\3y=-\dfrac{3}{4}\qquad\text{divide both sides by 3}\\\\\boxed{y=-\dfrac{1}{4}}

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Answer:

Step-by-step explanation:

Given as :

The distance cover while running = D_1 = 5 miles

Let The speed for running = S_1

The distance cover with bike = D_2 = 80 miles

The speed for biking = S_2 = 15 mph +  S_1

Total Time taken = 5 hours

Now Time = \dfrac{\textrm Distance}{\textrm Speed}

∴ 5 hour = \frac{D_1}{S_1} +  \frac{D_2}{S_2}

Or,  5 hour = \frac{5}{S_1} +  \frac{80}{15+S_1}

Or, 5 hour = \frac{75 + 5 S_1 + 80 S_1}{S_1(15+S_1)}

or,  5 × (S_1^{2}+15 S_1) = 85 S_1 + 75

Or, 5 S_1^{2} + 75 S_1 -  85 S_1 - 75 = 0

or, 5 S_1^{2} -10 S_1 - 75 = 0

or,   S_1^{2} -2 S_1 - 15 = 0

Or, S_1^{2} -3 S_1 + 5 S_1- 15 = 0

Or, S_1 (S_1 - 3) + 5 (S_1 - 3) = 0

Or, (S_1 - 3) ( S_1 + 5 ) = 0

∴ S_1 = 3 , - 5

So, the running speed = 3 mile per hour

And the biking speed = 15 mph + 3 mph = 18 mile per hour

Hence The running speed of Stu is 3 mile per hour  .  Answer

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A picture can help.

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