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astra-53 [7]
2 years ago
9

This system has one solution.

Mathematics
1 answer:
mel-nik [20]2 years ago
4 0

Answer:

<h2>y = 2</h2>

Step-by-step explanation:

y=8x-14\qquad(1)\\y=x^2+4x-10\qquad(2)\\\\\text{compare equations}\\\\x^2+4x-10=8x-14\qquad\text{subtract 8x from both sides}\\\\x^2-4x-10=-14\qquad\text{add 14 to both sides}\\\\x^2-4x+4=0\\\\x^2-2x-2x+4=0\\\\x(x-2)-2(x-2)=0\\\\(x-2)(x-2)=0\\\\(x-2)^2=0\iff x-2=0\qquad\text{add 2 to both sides}\\\\x=2\\\\\text{Put the value of x to (1)}:\\\\y=8(2)-14=16-14=2

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The choice which describes the solution is; The solution is 5, which represents the number of miles she runs each day.

<h3>Word problems</h3>

According to the task content;

  • The total distance covered running and cycling per day is; 20miles

  • Additionally, she cycles a total of 105 miles each week.

From the statement above; it follows that;

The number of miles she cycles per day since 7 days make a week is;

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Hence, it follows that the equation; (15+r) = 20 represents the daily distance covered by cycling and running.

On this note, it follows that;

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Hence, The solution is 5, which represents the number of miles she runs each day.

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