All categories

2 years ago

Use addition or substitution to find the value of y for this set of equations. 4x + 13y = 40 4x + 3y = -40

1 answer:

5 0

4x + 13y = 40
4x + 3y = -40

multiply second equation by -1

4x + 13y = 40
-4x - 3y = 40

add equations together

10y = 80
y = 8

put y in either original equation

4x + 3(8) = -40
4x + 24 = -40

subtract 24 from both sides

4x = 64

x=16
y=8

You might be interested in

Apply Crammer's Rule to find the solution to the following quations .2x + 3y = 1, 3x + y = 5

Bond [772]

Answer:

The solution to the equation system given is:

<u>x = 2</u>
<u>y = -1</u>

Step-by-step explanation:

First, we must know the equations given:

2x + 3y = 1
3x + y = 5

Following Crammer's Rule, we have the matrix form:

$\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] =\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}1\\5\end{array}\right]$

Now we solve using the determinants:

$x=\frac{\left[\begin{array}{ccc}1&3\\5&1\end{array}\right]}{\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] } =\frac{(1*1)-(5*3)}{(2*1)-(3*3)} = \frac{1-15}{2-9} =\frac{-14}{-7} = 2$

$y=\frac{\left[\begin{array}{ccc}2&1\\3&5\end{array}\right]}{\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] } =\frac{(2*5)-(3*1)}{(2*1)-(3*3)}=\frac{10-3}{2-9} =\frac{7}{-7}=-1$

Now, we can find the answer which is x= 2 and y= -1, we can replace these values in the equation to confirm the results are right, with the first equation:

2x + 3y = 1
2(2) + 3(-1)= 1
4 - 3 = 1
1 = 1

And, with the second equation:

3x + y = 5
3(2) + (-1) = 5
6 - 1 = 5
5 = 5

4 0

2 years ago

If you have $10, and you money doubles every year, how much money will you have in 10 years?

aleksandr82 [10.1K]

Answer:

Year 1: 10

Year 2: 20

Year 3: 40

Year 4: 80

Year 6: 160

Year 7: 320

Year 8: 640

Year 9: 1280

Year 10: 2560

8 0

2 years ago

Read 2 more answers

Dayren is driving to visit family. She drives at a average of 65 miles per hour. She drives 227.5 miles before lunch. And then 9

Kitty [74]

Answer:

5 hours

Step-by-step explanation:

First, add the miles together

Next, divide 65 into the sum of 227.5 and 97.5(which is 325)

8 0

2 years ago

Read 2 more answers

Part A

kkurt [141]

Answer:

Part A: A

Part B: A

Step-by-step explanation:

the inequality should be less than or equal to, since we need to find how many are left

now, the answer B is wrong, since there can't be negative 56, since Xander collected some cans, though he still must collect a few

thus, the answer is A

A again is correct, since it represents:c ≤ 56

B represents c ≥ 56

C represents c ≤ –56

D represents c ≥ -56

3 0

3 years ago

90°-56°=(x+6)° what is x

Mrrafil [7]

$Answer: \\ x + 6 = 90 - 56 \\ \Leftrightarrow x + 6 = 34 \\ \Leftrightarrow x = 28$

4 0

3 years ago

Read 2 more answers