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charle [14.2K]
3 years ago
8

Solve the simultaneous equations 8x+3y=45 2x+3y=27

Mathematics
1 answer:
Vedmedyk [2.9K]3 years ago
4 0

Answer:

x = 3 and y = 7

Step-by-step explanation:

Given that,

8x+3y=45 .......(1)

2x+3y=27 ........(2)

We need to solve equations (1) and (2)

Multiply equation (2) by 4.

8x+12y=108 .....(3)

Subtract equation (1) from (3).

8x+12y-(8x+3y)=108-45

12y-3y = 63

9y = 63

y = 7

Put the value of y in equation (1).

2x+3(7)=27

2x+21 = 27

2x = 27-21

2x = 6

x = 3

So, the values of x and y are 3 and 7 respectively.

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Two cars traveled equal distances in different amounts of time. Car A traveled the distance in 2 h, and Car B traveled the dista
irakobra [83]

Answer: Car B traveled 60 mph.

Step-by-step explanation:

A= B-15

A: (B - 15)(2 hr)=D

B: (B)(1.5)=D

Since B and A traveled the same distance you can plug in 1.5B for D.

2B - 30 = 1.5B

-1.5B +30 = -1.5B

——————+30—

2(0.5B) = 2(30)

B = 60 mph

4 0
3 years ago
Read 2 more answers
If (ax+2)(bx+7)=15x2+cx+14 for all values of x, and a+b=8, what are the 2 possible values fo c
dolphi86 [110]

Given:

(ax+2)(bx+7)=15x^2+cx+14

And

a+b=8

Required:

To find the two possible values of c.

Explanation:

Consider

\begin{gathered} (ax+2)(bx+7)=15x^2+cx+14 \\ abx^2+7ax+2bx+14=15x^2+cx+14 \end{gathered}

So

\begin{gathered} ab=15-----(1) \\ 7a+2b=c \end{gathered}

And also given

a+b=8---(2)

Now from (1) and (2), we get

\begin{gathered} a+\frac{15}{a}=8 \\  \\ a^2+15=8a \\  \\ a^2-8a+15=0 \end{gathered}a=3,5

Now put a in (1) we get

\begin{gathered} (3)b=15 \\ b=\frac{15}{3} \\ b=5 \\ OR \\ b=\frac{15}{5} \\ b=3 \end{gathered}

We can interpret that either of a or b are equal to 3 or 5.

When a=3 and b=5, we have

\begin{gathered} c=7(3)+2(5) \\ =21+10 \\ =31 \end{gathered}

When a=5 and b=3, we have

\begin{gathered} c=7(5)+2(3) \\ =35+6 \\ =41 \end{gathered}

Final Answer:

The option D is correct.

31 and 41

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1 year ago
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3 years ago
What is the equation of a line that has a slope of -2 and goes through the origin?
UkoKoshka [18]

Answer:y = -2x


Step-by-step explanation:

slope-intercept form is as follows

y = mx + b

You are given that the slope is -2 and since the line passes through the origin, there is no y-intercept

So you just plug in the slope

y = -2x + b

And since there is no y-intercept, you can take that out.

y = -2x

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3 years ago
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