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dybincka [34]
2 years ago
11

If y-3x=9, 7x+y=25, what is the value of x and y?

Mathematics
1 answer:
lianna [129]2 years ago
4 0

\bold{\rm{Given}}\text{ : If y - 3x = 9, 7x + y = 25, what is the value of x and y}?

\bold{\rm{Solution}} \text{: We'll solve this by substitution method}

\dashrightarrow  y - 3x = 9 \\  \\  \dashrightarrow   \boxed{y = 9 + 3x } \qquad .. \sf eq(1)

\text{we got the value of y now getting the value of x}

\looparrowright 7x + y = 25 \\  \\  \looparrowright 7x = 25 - y \\  \\  \looparrowright  \boxed{x =   \frac{25 - y}{7}} \qquad .. \sf eq(2)

\text{Now, putting y = 9 + 3x in eq(2)}

\hookrightarrow  x =  \frac{25 - y}{7}   \\  \\ \hookrightarrow  x =  \frac{25 - 9 + 3x}{7}  \\  \\ \hookrightarrow  7x =  25 - 9 + 3x \\  \\ \hookrightarrow  7x - 3x =  16 \\  \\ \hookrightarrow  4x = 16 \\  \\ \hookrightarrow  x =  \frac{16}{4}  \\  \\ \star \quad  \boxed{ \green{ \frak{ x = 4}}}

\text{Now we know the value of x, for getting y we need to put x in eq(1)}

: \implies y = 9 + 3x \\  \\   : \implies y = 9 + 3(4) \\  \\  : \implies y = 9 + 12  \\  \\    \star \quad  \boxed{\frak{  \green{y = 21}}}

\text{Hence, values of x and y are} \:  \frak{ \green{4}}  \: \text{and} \:  \frak{ \green{21}} \: \text{respectively}.

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A bus driver pays all tolls, using only nickels and dimes, by throwing one coin at a time into the mechanical toll collector.
lutik1710 [3]

Answer: a) An = An-1 + An-2

b) 55ways

Step-by-step explanation:

a) a nickel is 5 cents and a dime is 10cent so a multiple of 5 cents is the possible way to pay the tolls in both choices.

Let An represents the number of possible ways the driver can pay a toll of 5n cents, so that

An = 5n cents

Case 1: Using a nickel for payment which is 5 cents, the number of ways given as;

An-1 = 5( n-1)

Case 2: using a dime which is two 5 cents, the number of ways is given as;

An-2 = 5(n-2)

Summing up the number of ways, we have

An = An-1 + An-2

From the relation,

If n= 0, Ao= 1

n =1, A1= 1

b) 45 cents paid in multiples of 5cents will give us 9 ways(A9)

From the relation, we have that

Ao = 1

A1 = 1

An =An-1 + An-2

Ao = 1

A1 = 1

A2 = A1+Ao = 1+1= 2

A3 = A2 + A1 = 3

A4 = A3+A2=5

A5=A4+A3=8

A6=A5+A4=13

A7 =A6+A5 = 21

A8= A7+A6= 34

A9= A8+A7= 55

So there are 55ways to pay 45cents.

4 0
2 years ago
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ivann1987 [24]
I think it’s 700, but I’m not positive
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2 years ago
Steve buys 21lbs of grapefruit and 3lbs of oranges for $7.20. Kennedy buys 4lbs of grapefruit and 2lbs or oranges for $8.80. How
dalvyx [7]

Answer:

19.6

Step-by-step explanation:

21+3=24

24-7.20=16.8

4+2=6

6-8.80=-2.8

19.6

7 0
3 years ago
Read 2 more answers
Please help!!! I can't figure it out​
weeeeeb [17]

A) From the given graph, we can see that the point where graph functions p(x) and f(x) intersect is seen to be;

x = 1, y = 5.0125

B) The possible solutions of the given equation will be; x = 3.11 or -3.11

C) The solution to p(x) = g(x) is; x = 0 and y = 0

<h3>How to find the solution to simultaneous equations graphically?</h3>

When we are trying to solve two simultaneous equations, there are three methods we can use namely;

1) Elimination Method

2) Substitution Method

3) Graphical Method

Now, we see that we are to use the graphical method from the given graph.

Now, the solution to the given pair of equation will be the coordinates of the points where both graphs intersect.

A) From the given graph, we can see that the point where graph functions p(x) and f(x) intersect is seen to be;

x = 1, y = 5.0125

B) The possible solutions of the given equation will be the point where f(x) = 0 which is where the line crosses the x-axis and so we have;

x = 3.11 or -3.11

C) The solution to p(x) = g(x) is the coordinate;

x = 0 and y = 0

Read more about Simultaneous Equations Solutions at; brainly.com/question/16863577

#SPJ1

7 0
1 year ago
The quotient of twice a number t and 12
Arisa [49]
(t + 12) ^ 2
(t + 12) (t + 12)
t ^ 2 + 12t + 12t + 144 144 24
t ^ 2 + 24t + 144 -------|--------
(t + 12) (t + 12) = 0 12,12 | 24

t = -12
5 0
3 years ago
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