MATHEMATICS HIGH SCHOOL

How to solve linear equations by substitution?

5x+2y=9
x+y=-3

Answers

Answer 1

Answer:

5x+2y=9 x+y=3

change x+y=3 into x=3-y

plug that equation into 5x+2y=9 where x is.

5(3-y)+2y=9

then distribute.

15-5y+2y=9

15-7y=9

minus 15.

-7y=-6

divide both sides by -7.

y is equal to -6/7.

then go back to the first equation and plug in for y.

and then you will get x.

then you will have (y,x)

Answer 2

Answer: $\begin{cases} 5x+2y=9 \n x+y=-3\end{cases} \n \n\begin{cases} 5x+2*(-3-x)=9 \n y=-3 -x\end{cases} \n \n\begin{cases} 5x-6-2x =9 \n y=-3 -x\end{cases}\n \n\begin{cases} 3x =9+6 \n y=-3 -x\end{cases}$

$\begin{cases} 3x =15 \ \ /:3 \n y=-3 -x\end{cases} \n \n\begin{cases} x =5 \n y=-3 -5\end{cases} \n \n\begin{cases} x =5 \n y=-8\end{cases}$

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A motorist traveled 311 miles on 12 gallons of gas. To the nearest tenth, how many miles can the motorist travel on one gallon of gas?

Answers

we know that
by using proportion
$(311 miles)/(12 gallons) = (x miles)/(1 gallon) \n x= (31.1)/(12) \n x=25.9 miles$

the answer is
$25.9 miles$

Number of miles that can be traveled on one gallon of gas=311/12
=25.92miles
=25.9miles(to the nearest tenth)

Write the equation of the line that passes through the given point and is parallel to the given line. Write the answer in slope-intercept formP(-6,3), y + 3x = -12
Can anyone help me on this one? Thanks!

Answers

$General\ formula:\ny=ax+b\n\ny+3x=-12\ny=-3x-12\n\nLine\ is\ parallel\ to\ the\ given\ when\ a=-\-3}\ny=-3x+b\n\nPasses\ through\ P(-6,3):\n3=(-3)*(-6)+b\n3-18=b\nb=-15\n\nAnswer:\ y=-3x-15$

Brad spent 20 percent of his money to buy a car costing £6800 how much did he havePlease reply asap

Answers

He had 34000 euros total. Divide 6800 by 0.2 (AKA 20%)

There are few ways but i prefere this way:

100/20=5
6800*5=?
6000*5=30000
800*5= 4000
+-----------
= 34000

=£34000

C = 0.765x + 0.06(0.765x)

Answers

Hey there!

$c=0.765x+0.06(0.765x)$

Add:

$c=0.765x+0.06(0.765x)\nc=0.8109x$

Hope this helps!

$AT2309$

7x+3y=22 4y=20 I need to know how to write this equation out with the answer

Answers

$\begin{cases} 7x+3y=22 \n 4y=20 \ \ /:4 \end{cases}\n \n\begin{cases} 7x+3 \cdot 5=22 \n y= 5 \end{cases}\n \n\begin{cases} 7x+15=22 \ \ |-15 \n 4y=20 \end{cases}$

$\begin{cases} 7x+15 -15=22 -15 \n y=5 \end{cases}\n \n\begin{cases} 7x =7\ \ / :7 \n y=5 \end{cases}\n \n\begin{cases} x =1 \n y=5 \end{cases}\n \n$

7x+3y=22
4y=20

4y=20
y=5

Substitute to first equation
7x+15=22
7x=7
x=1

Find the reciprocal of the number. Multiply to check your answer. The number is 6. A. 1/6 B. 1 C. 12 D. 36