1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Karo-lina-s [1.5K]
3 years ago
11

For what value of a should you solve the system of elimination?

Mathematics
2 answers:
SIZIF [17.4K]3 years ago
7 0
\begin{bmatrix}3x+5y=10\\ 2x+ay=4\end{bmatrix}

\mathrm{Multiply\:}3x+5y=10\mathrm{\:by\:}2: 6x+10y=20
\mathrm{Multiply\:}2x+ay=4\mathrm{\:by\:}3: 3ay+6x=12

\begin{bmatrix}6x+10y=20\\ 6x+3ay=12\end{bmatrix}

6x + 3ay = 12
-
6x + 10y = 20
/
3a - 10y = -8

\begin{bmatrix}6x+10y=20\\ 3a-10y=-8\end{bmatrix}

3a-10y=-8 \ \textgreater \  \mathrm{Subtract\:}3a\mathrm{\:from\:both\:sides}
3a-10y-3a=-8-3a

\mathrm{Simplify} \ \textgreater \  -10y=-8-3a \ \textgreater \  \mathrm{Divide\:both\:sides\:by\:}-10
\frac{-10y}{-10}=-\frac{8}{-10}-\frac{3a}{-10}

Simplify more.

\frac{-10y}{-10} \ \textgreater \  \mathrm{Apply\:the\:fraction\:rule}: \frac{-a}{-b}=\frac{a}{b} \ \textgreater \  \frac{10y}{10}

\mathrm{Divide\:the\:numbers:}\:\frac{10}{10}=1 \ \textgreater \  y

-\frac{8}{-10}-\frac{3a}{-10} \ \textgreater \  \mathrm{Apply\:rule}\:\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c} \ \textgreater \  \frac{-8-3a}{-10}

\mathrm{Apply\:the\:fraction\:rule}: \frac{a}{-b}=-\frac{a}{b} \ \textgreater \  -\frac{-3a-8}{10} \ \textgreater \  y=-\frac{-8-3a}{10}

\mathrm{For\:}6x+10y=20\mathrm{\:plug\:in\:}\ \:y=\frac{8}{10-3a} \ \textgreater \  6x+10\cdot \frac{8}{10-3a}=20

10\cdot \frac{8}{10-3a} \ \textgreater \  \mathrm{Multiply\:fractions}: \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c} \ \textgreater \  \frac{8\cdot \:10}{10-3a}
\mathrm{Multiply\:the\:numbers:}\:8\cdot \:10=80 \ \textgreater \  \frac{80}{10-3a}

6x+\frac{80}{10-3a}=20 \ \textgreater \  \mathrm{Subtract\:}\frac{80}{10-3a}\mathrm{\:from\:both\:sides}
6x+\frac{80}{10-3a}-\frac{80}{10-3a}=20-\frac{80}{10-3a}

\mathrm{Simplify} \ \textgreater \  6x=20-\frac{80}{10-3a} \ \textgreater \  \mathrm{Divide\:both\:sides\:by\:}6 \ \textgreater \  \frac{6x}{6}=\frac{20}{6}-\frac{\frac{80}{10-3a}}{6}

\frac{6x}{6} \ \textgreater \  \mathrm{Divide\:the\:numbers:}\:\frac{6}{6}=1 \ \textgreater \  x

\frac{20}{6}-\frac{\frac{80}{10-3a}}{6} \ \textgreater \  \mathrm{Apply\:rule}\:\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c} \ \textgreater \  \frac{20-\frac{80}{-3a+10}}{6}

20-\frac{80}{10-3a} \ \textgreater \  \mathrm{Convert\:element\:to\:fraction}: \:20=\frac{20}{1} \ \textgreater \  \frac{20}{1}-\frac{80}{-3a+10}

\mathrm{Find\:the\:least\:common\:denominator\:}1\cdot \left(-3a+10\right)=-3a+10

Adjust\:Fractions\:based\:on\:the\:LCD \ \textgreater \  \frac{20\left(-3a+10\right)}{-3a+10}-\frac{80}{-3a+10}

\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}: \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}
\frac{20\left(-3a+10\right)-80}{-3a+10} \ \textgreater \  \frac{\frac{20\left(-3a+10\right)-80}{-3a+10}}{6} \ \textgreater \  \mathrm{Apply\:the\:fraction\:rule}: \frac{\frac{b}{c}}{a}=\frac{b}{c\:\cdot \:a}

20\left(-3a+10\right)-80 \ \textgreater \  Rewrite \ \textgreater \  20+10-3a-4\cdot \:20

\mathrm{Factor\:out\:common\:term\:}20 \ \textgreater \  20\left(-3a+10-4\right) \ \textgreater \  Factor\;more

10-3a-4 \ \textgreater \  \mathrm{Subtract\:the\:numbers:}\:10-4=6 \ \textgreater \  -3a+6 \ \textgreater \  Rewrite
-3a+2\cdot \:3

\mathrm{Factor\:out\:common\:term\:}3 \ \textgreater \  3\left(-a+2\right) \ \textgreater \  3\cdot \:20\left(-a+2\right) \ \textgreater \  Refine
60\left(-a+2\right)

\frac{60\left(-a+2\right)}{6\left(-3a+10\right)} \ \textgreater \  \mathrm{Divide\:the\:numbers:}\:\frac{60}{6}=10 \ \textgreater \  \frac{10\left(-a+2\right)}{\left(-3a+10\right)}

\mathrm{Remove\:parentheses}: \left(-a\right)=-a \ \textgreater \   \frac{10\left(-a+2\right)}{-3a+10}

Therefore\;our\;solutions\;are\; y=\frac{8}{10-3a},\:x=\frac{10\left(-a+2\right)}{-3a+10}

Hope this helps!
Novay_Z [31]3 years ago
7 0
--------------------------
3x + 5y = 10:


1. Subtract 5y from both sides

3x = 10 - 5y

2. Divide both sides by 3

x = 10 - 5y over 3

3. Factor out the common term 5

x = 5(2 - y) over 3

Final Answer:

x = 5(2 - y) over 3
-----------------------------
2x + ay = 4

1. Subtract ay from both sides

2x = 4 - ay

2. Divide both sides by 2

x = 4 - ay over 2

Final Answer:

x = 4 - ay over 2
You might be interested in
Which line is parallel to y = -4x + 8?
Musya8 [376]
Y = -4x + 3
Because, it has the same slope (-4) as the slope of y = -4x + 8
5 0
3 years ago
The cost to rent a car is $25 plus an additional $0.15 for each mile the car is driven. Which of the following equations could b
kirill [66]

Answer:

25 + 0.15m = 71.8

Step-by-step explanation:

Given:

Fixed charge = $25

Additional charge for each mile = $0.15

Let number of miles driven be m.

Total Billed amount = $71.80

Now total bill amount is calculated by adding fixed charge with additional charge for each mile times number of miles.

Hence,

Total Billed amount  = Fixed charge + Additional charge for each mile × number of miles driven

25 + 0.15m = 71.8

Hence the equation is 25 + 0.15m = 71.8.

3 0
3 years ago
If H be the H.M. between a and b.<br> prove that 1/H-a + 1/H-b = 1/a+1/b​
____ [38]

if susjwmaoakkaajKIJahabsbzh

3 0
2 years ago
Help me please and thanks
Arturiano [62]

This is the answer its easy just simplify the inequality

3 0
3 years ago
Symplify the expression 3⁴÷3⁹. Select all that apply.​
LenKa [72]

Answer: answer is C and D when dividing exponents you subtract and with negatives you turn it into a fraction

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
Other questions:
  • SOMEONE PLS HELP ME WITH THIS: Jack Thomas has an fudge sundae with 450 calories. How long would it take him to burn off the cal
    7·2 answers
  • What is the monetary amount of 222 quarters
    9·1 answer
  • What is the average of 69 and 50?<br>PLEASE HELP<br>​
    10·1 answer
  • Please select the word from the list that best fits the definition
    9·1 answer
  • It took a plane 2 hours to go from Dallas to NY with the head wind and 1.5 hours to get back with the tail wind. If the speed of
    6·1 answer
  • Astronauts who traveled to the moon were able to float slightly as they walked along its surface. Why wee the astronauts able to
    11·1 answer
  • 0<br> 100%<br> Which expression is equivalent to (-11x2 +1.4x-3) + (4x2-2.7x+8)
    14·1 answer
  • 2x^2y^5 + 4xy^3 please answer
    11·1 answer
  • Help me please like plase
    12·1 answer
  • A dragon has been wreaking havoc n a local village. It is then chased away by a knight. The dragon flies 3miles due south follow
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!