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xenn [34]
3 years ago
12

Solve t/he system of linear equations given by x + y = 1 and ax − by = c, where a, b, c are real numbers. Note: The solution in

this case will not be numbers but formulas containing a, b, and c. Need help ASAP!!
Mathematics
1 answer:
Phantasy [73]3 years ago
8 0

Answer:

see explanation

Step-by-step explanation:

Given the 2 equations

x + y = 1 → (1)

ax - by = c → (2)

In (1) subtract y from both sides

x = 1 - y → (3)

Substitute x = 1 - y into (2)

a(1 - y) - by = c ← distribute left side

a - ay - by = c ( subtract a from both sides )

- ay - by = c - a ( multiply through by - 1 )

ay + by = a - c ← factor out y from each term on the left side

y(a + b) = a - c ← divide both sides by (a + b)

y = \frac{a-c}{a+b} ← substitute into (3)

x = 1 - \frac{a-c}{a+b} = \frac{a+b}{a+b} - \frac{a-c}{a+b} = \frac{a+b-a+c}{a+b} = \frac{b+c}{a+b}

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16% of 150 is what number plz show work
bazaltina [42]
To get the solution, we are looking for, we need to point out what we know. 

<span>1. We assume, that the number 150 is 100% - because it's the output value of the task. </span>
<span>2. We assume, that x is the value we are looking for. </span>
<span>3. If 150 is 100%, so we can write it down as 150=100%. </span>
<span>4. We know, that x is 16% of the output value, so we can write it down as x=16%. </span>
5. Now we have two simple equations:
1) 150=100%
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where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
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6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for what is 16% of 150

150/x=100/16
<span>(150/x)*x=(100/16)*x       - </span>we multiply both sides of the equation by x
<span>150=6.25*x       - </span>we divide both sides of the equation by (6.25) to get x
<span>150/6.25=x </span>
<span>24=x </span>
x=24

<span>now we have: </span>
<span>16% of 150=24</span>
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