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
mars1129 [50]
3 years ago
14

How do i solve this solution: 2x+4y=-7 4x-2y=6

Mathematics
1 answer:
exis [7]3 years ago
5 0

Answer:

hope this helps ✌

MULTIPLY THE FIRST EQUATION BY -2 & ADD THEM.

-4X+8Y=-14

4X-2Y=9

6Y=-5

Y=-5/6 ANSWER.

4X-2*-5/6=9

4X+10/6=9

Step-by-step explanation:

Lets start with the given system of linear equations

2%2Ax-4%2Ay=7

4%2Ax-2%2Ay=9

In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa).

So lets eliminate x. In order to do that, we need to have both x coefficients that are equal but have opposite signs (for instance 2 and -2 are equal but have opposite signs). This way they will add to zero.

So to make the x coefficients equal but opposite, we need to multiply both x coefficients by some number to get them to an equal number. So if we wanted to get 2 and 4 to some equal number, we could try to get them to the LCM.

Since the LCM of 2 and 4 is 4, we need to multiply both sides of the top equation by 2 and multiply both sides of the bottom equation by -1 like this:

2%2A%282%2Ax-4%2Ay%29=%287%29%2A2 Multiply the top equation (both sides) by 2

-1%2A%284%2Ax-2%2Ay%29=%289%29%2A-1 Multiply the bottom equation (both sides) by -1

So after multiplying we get this:

4%2Ax-8%2Ay=14

-4%2Ax%2B2%2Ay=-9

Notice how 4 and -4 add to zero (ie 4%2B-4=0)

Now add the equations together. In order to add 2 equations, group like terms and combine them

%284%2Ax-4%2Ax%29-8%2Ay%2B2%2Ay%29=14-9

%284-4%29%2Ax-8%2B2%29y=14-9

cross%284%2B-4%29%2Ax%2B%28-8%2B2%29%2Ay=14-9 Notice the x coefficients add to zero and cancel out. This means we've eliminated x altogether.

So after adding and canceling out the x terms we're left with:

-6%2Ay=5

y=5%2F-6 Divide both sides by -6 to solve for y

y=-5%2F6 Reduce

Now plug this answer into the top equation 2%2Ax-4%2Ay=7 to solve for x

2%2Ax-4%28-5%2F6%29=7 Plug in y=-5%2F6

2%2Ax%2B20%2F6=7 Multiply

2%2Ax%2B10%2F3=7 Reduce

2%2Ax=7-10%2F3 Subtract 10%2F3 from both sides

2%2Ax=21%2F3-10%2F3 Make 7 into a fraction with a denominator of 3

2%2Ax=11%2F3 Combine the terms on the right side

cross%28%281%2F2%29%282%29%29%2Ax=%2811%2F3%29%281%2F2%29 Multiply both sides by 1%2F2. This will cancel out 2 on the left side.

x=11%2F6 Multiply the terms on the right side

So our answer is

x=11%2F6, y=-5%2F6

which also looks like

(11%2F6, -5%2F6)

Notice if we graph the equations (if you need help with graphing, check out this solver)

2%2Ax-4%2Ay=7

4%2Ax-2%2Ay=9

we get

graph of 2%2Ax-4%2Ay=7 (red) 4%2Ax-2%2Ay=9 (green) (hint: you may have to solve for y to graph these) and the intersection of the lines (blue circle).

and we can see that the two equations intersect at (11%2F6,-5%2F6). This verifies our answer.You really don't want to solve this system by 'addition.' What you want is to solve it by elimination, using addition as one of the steps of the process.

The idea of solving by elimination is to multiply (if necessary) one of the equations by some constant so that one of the variables will have a coefficient that is the additive inverse of the coefficient on the same variable in the other equation.

In this example, multiply the first equation by -2, resulting in a coefficient on the x term of -4. -4 is the additive inverse of the 4 coefficient on x in the second equation.

-4x+%2B+8y+=+-14

4x-2y=9

Now you can add the two equations, term-by-term. That is, you add the x terms to the x terms, the y terms to the y terms, and the constants to the constants, resulting in one equation with a zero coefficient on one of the variables, in this case, x.

The sum equation is:

0x%2B6y=-5

Divide by 6:

y=-%285%2F6%29

Now that you have a value for y, you can either substitute that value into either one of the original equations and solve for x, or you could take the original two equations, multiply one of them by an appropriate constant to eliminate the y variable so that you can solve for x. Either way works. Watch carefully:

4x-2%28-5%2F6%29=9

4x%2B5%2F3=9

4x=%2827%2F3%29-%285%2F3%29

4x=22%2F3

x=11%2F6

You might be interested in
The answer to this equation​
12345 [234]

Answer:

x=3

Step-by-step explanation:

We are given the equation

log5x=log(2x+9)

This can be rewritten as

log5x-log(2x+9)=0

Now using the quotient rule for logarithms we can combine these two

log(\frac{5x}{2x+9} )=0

Next we can remove the log by using an inverse operation

10^{log(\frac{5x}{2x+9} )} =10^0\\\\\frac{5x}{2x+9}=1

Now we can solve for x

\frac{5x}{2x+9}=1\\\\5x=2x+9\\\\3x=9\\\\x=3

4 0
3 years ago
3<br> Solve y - 18 = -3.<br> a) 15<br> 6<br> b) 21<br> 9<br> Oc) -21<br> 12<br> d) -15
Phantasy [73]
The answer d)
Explaining
y = -18 + 3
y= -15
8 0
3 years ago
Read 2 more answers
How do you write an exact angle measure without approximating to a decimal value?
dimulka [17.4K]

an exact angle measure without approximating to a decimal value is given below.

Step-by-step explanation:

Since an angle of 2 has degree measure 360° it follows that an angle of 1 radian has degree measure (180/ )°. Likewise, an angle of size 1° has radian measure /180. We now can easily obtain a formula to convert from degrees to radians and vice-versa. To convert from degrees to radians, multiply the angle by /180.

convert decimal degrees to DMS :

  • For the degrees use the whole number part of the decimal.
  • For the minutes multiply the remaining decimal by 60. Use the whole number part of the answer as minutes.
  • For the seconds multiply the new remaining decimal by 60.
4 0
2 years ago
Can anyone help me with this problem. This question is a little hard. Is anyone on to help. Can’t understand
exis [7]

Answer: It should be D if im looking at this correctly

Step-by-step explanation:

Plain and simple

7 0
1 year ago
Read 2 more answers
What is the value of b?
labwork [276]
The value of b is 61°.

you solve by doing this:
add up the two given angles, 58° and 61° to get 119°. then you subtract from 180° to get 61.
4 0
3 years ago
Read 2 more answers
Other questions:
  • If 9 = 5 + 4 and 5 + 4 = 3 + 6, then 9 = 3 + 6. This is an example of which property?
    7·2 answers
  • HELP ME DUE TODAY 90 POINTS AND A BRAINLIST
    14·1 answer
  • The area of a square can be expressed by the polynomial expression 16x^4 -16x^2 +4. What is the polynomial expression for the le
    14·1 answer
  • Five less than 25% of a number is twice the difference of the number and 14. Write an equation that could be used to find the nu
    11·1 answer
  • 2.2.17<br> Given the function H(v) = 10v +9, find each of the following.<br> H(3) =
    10·1 answer
  • A triangle has an area of 36 cm². The base and height are scaled by a factor of 5.
    11·1 answer
  • Ling's elementary school principal wants to hire some new teachers. 6 teachers applied for one 1st grade teaching job, and 3 tea
    8·1 answer
  • How to the medium in the dot line????!! I don't want my mom to be mad at my grade please!!!!!!
    7·1 answer
  • A local hamburger shop sold a combined total of 394 hamburgers and cheeseburgers on Wednesday. There were 56 fewer cheeseburgers
    7·1 answer
  • 50 Points!!! Is there a difference between the Side-Side-Side theorem and Side-Side-Side postulate? Yes or no? Explain.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!