Call the two equations above A and B, in order to not confuse them.
A: -2x + 6y = -38
B: 3x - 4y = 32
For this system we have opposites in x and y, so Elimination (or Linear Combination) works best. Either variable works, so let's work with x first and multiply A by 3 and B by 2. This is done so we get opposites in A and B then when added together give zero.
-2x + 6y = -38 ------> multiply by 3 ----> -6x + 18y = -114
3x - 4y = 32 ------> multiply by 2 -----> 6x - 8y = 64
Now we add the new equations. The -6x and 6x are opposites and go away. We are left with
10y = -50. We divide both sides by 10 and get that y = -5.
Now we take y = -5 and put it into an original equation. Let's use A.
-2x + 6y = -38 the original equation A
-2x + 6(-5) = -38 we found y = -5
-2x + (-30) = -38 evaluating and multiplying
-2x - 30 = -38 apply the parentheses
-2x = -8 add 30 to both sides
x = 4 divide on both sides by -2
Thus x = 4 and y = -5, or (4, -5) is the solution.
Answer:
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The delivery person will use 6 gallons of gasoline
The function to determine the number of miles in x hours is:
f(x) = x² + 3x
The number of gallons of gasoline used for driving y miles is:
g(y) = y/18
For a delivery person that works a 9-hour shift:
x = 9
f(9) = 9² + 3(9)
f(9) = 81 + 27
f(9) = 108
That is, the number of miles, y = 108 miles
The number of gallons of gasoline used:
g(y) = y/18
g(108) = 108/18
g(108) = 6
The delivery person will use 6 gallons of gasoline
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Answer:
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