Question

How to solve a+9b=11 and a+2b=-3 using the elimination method

Answer 1

just subtract the second equation from the first to eliminate a
then solve for b
finally plug in this value of b into one of the equation to find a

Answer 2

U got to find the answers to a and b

Answer 3

a+9b=11(equation 1)
a+2b=-3 (euation 2)
- - +
---------
7b=14

7b=14
b=14/7
b=2
Now find the value if a by putting the value of b in equation 1
a+9b=11
a+9(2)=11
a+18=11
a=11-18
a=-7

So, a =-7 and b=2

Answer 4

thank you so much

Answer 5

Slightly different method would be to multiply one of the equations by -1, then add. If you have a tendency to make mistakes when subtracting negative quantities, this may safer.

Answer 6

Your welcome :) @mackdiesel27 you can even verify your answer. If you want to know how I'll tell you :)

Answer 7

that would be great.

Answer 8

@xoya Wow :o You're nice,never knew hehe.

Answer 9

You so listen first we will take equation 1 that is
a+9b=11
Then we will put the values of a and b both in the equation
-7+9(2)=11
-7+18=11
11=11
Both the sides should be equal if they are so your answer is correct
Now take equation 2 that is
a+2b=-3
Do same put the values in it
-7+2(2)=-3
-7+4=-3
-3=-3
So, this means your answer is correct :)

Answer 10

Thanks @uri

Answer 11

no thank you

Answer 12

hello have another couple of questions, I am terrible with graphing as well. It has been forever taking algebra. In shading the solution set of of the systems of inequalities, what is x+3y> -2 and 3x+y<_5

Answer 13

Okay, here's how I do these. First, convert them to equalities, to get the equation of the line that borders the region. Then, test a point to figure out which portion to shade.
\[x+3y=-2\]Now, find the x and y intercepts by alternately setting x and y = 0 and solving for the other variable. \[0+3y=-2\]\[y=-2/3\]\[x+3(0)=-2\]\[x=-2\]That means our line goes through (0,-2/3) and (-2,0).

Now the other line:
\[3x+y=5\]
\[3(0)+y=5\]\[y=5\]
\[3x+0=5\]\[x=5/3\]
So this line goes through (0,5) and (5/3,0)

Answer 14

wow that is crazy i was way off. i am also taking accounting and trying to figure this out as well.

Answer 15

Now, figure out which area to shade. I like to use (0,0) as a test point, because the arithmetic is usually very easy. I substitute (0,0) into each inequality and see if it makes the inequality true. If it does, then (0,0) is in the area to be shaded. If not, then the section across the line from (0,0) is shaded.

\[x+3y>-2\]\[0+3(0)>-2\checkmark\]
\[3x+y\le5\]\[3(0)+0\le 5\checkmark\]
So the wedge extending up to the left which includes the origin (0,0) is the area that satisfies the inequalities. And because the first inequality had > rather than >=, we use a dashed line for it because it does not include the points on the line.

Answer 16

An easy way to remember that is if the inequality sign has a line under it, you draw a line under the dashes, giving you a solid line :-)

Answer 17

It gets easier with practice...

Answer 18

thanks so much. i just want to get better because its not any easier. I also have a word problem with percentages. i keep getting the concept mixed up. the problem is an investor invested a total of 1700 dollars with a 9% percent profit in one and 2% in another. if the total profit is 125 how much is in both mutual funds?

Answer 19

Oh, I like these :-)

Let's call one fund N (earns 9%) and the other T (earns 2%)

N+T = 1700
0.09N + 0.02T = 125

Can you solve that system of equations?

Answer 20

0.09N just means 9% of N. 0.02T is 2% of T. Does the setup make sense to you?

Answer 21

Now once you have solved for N and T, note that that is the amount you invested, and the amount in the fund at the end is going to be N + 0.09N and T + 0.02T...

Answer 22

Do you want me to go through the steps?

Answer 23

please?

Answer 24

Okay. Do you agree with the setup?

Answer 25

yes

Answer 26

Good :-)
\[N+T = 1700\]\[0.09N + 0.02T = 125\]Multiply the second one by 100 to clear the decimals\[9N+2T=12500\]Now solve the first one for \(N\) and substitute into the other:
\[N=1700-T\]\[9(1700-T)+2T=12500\]\[15300-9T+2T=12500\]\[7T=2800\]\[T=400\]\[N=1700-T=1700-400=1300\]
Check our work: \[0.09(1300)+0.02(400) = 117.00 + 8.00 = 125\checkmark\]

Okay, so initial balance in N was 1300. We earned 9%, so we now have 1300 + 9%*1300 = 1300+0.09*1300 = 1300+117=1417

Initial balance in T was 400, we earned 2%, so now have 400+2%*400=400+0.02*400=408.

Clear as mud?

Answer 27

lol. clear as mud? i like that.... i will get it together thank you so much.

Answer 28

Do you understand how I solved the equations?

Answer 29

yes with the breakdown i definitely got it together. I had this tutor and they seemed like they didnt really want to help. I am truly grateful for your help:)

Answer 30

Okay, I wasn't sure if you were saying "yes, I see how this works" or just wanting it all to go away like a bad dream :-)

Answer 31

thank you again