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monitta
3 years ago
6

Solve the system of equations by substitution. y = 8 X – 2y + 3z = 3 3x + 3y – 2z = 15

Mathematics
1 answer:
Dafna1 [17]3 years ago
6 0

Answer:

Solving systems of equations with 3 variables is very similar to how we solve systems with two variables. When we had two variables we reduced the system down

to one with only one variable (by substitution or addition). With three variables

we will reduce the system down to one with two variables (usually by addition),

which we can then solve by either addition or substitution.

To reduce from three variables down to two it is very important to keep the work

organized. We will use addition with two equations to eliminate one variable.

This new equation we will call (A). Then we will use a different pair of equations

and use addition to eliminate the same variable. This second new equation we

will call (B). Once we have done this we will have two equations (A) and (B)

with the same two variables that we can solve using either method. This is shown

in the following examples.

Example 1.

3x +2y − z = − 1

− 2x − 2y +3z = 5 We will eliminate y using two different pairs of equations

5x +2y − z = 3

Step-by-step explanation:

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Jamian bought a total of 35 bagels and donuts for a morning meeting. He paid a total of $36.25. Each donut cost $0.75 and each b
garri49 [273]

Answer: Jamian bought 20 bagels and 15 donuts

Step-by-step explanation:

Using the equation below:

b + d = 35 ...... i

1.25b + 0.75d = 36.25 ....... ii

Multiply i by 1.25

Multiply ii by 1

1.25b + 1.25d = 43.75 ...... iii

1.25b + 0.75d = 36.25 ....... iv

Subtract iv from iii

0.50d = 7.50

d = 7.50 / 0.50

d = 15

Since b + d = 35

b = 35 - 15

b = 20

Jamian bought 20 bagels and 15 donuts

8 0
3 years ago
Write the equation of the line through the points (2,4)(-3,-1). write answer in a point slope form
luda_lava [24]

Answer:

The point-slope form would be y - 4 = x - 2

Step-by-step explanation:

In order to find the equation of the line, we first need to find the slope. For that, we use the slope formula.

m (slope) = (y1 - y2)/(x1 - x2)

Now we plug the numbers into the equation.

m (slope) = (y1 - y2)/(x1 - x2)

m (slope) = (4 - -1)/(2 - -3)

m (slope) = 5/5

m (slope) = 1

Now we can use point-slope form along with the slope and either point to write the equation.

y - y1 = m(x - x1)

y - 4 = (x - 2)

3 0
3 years ago
Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to sta
Dafna11 [192]

Answer:  <em>r</em> represents a significant linear correlation.

Step-by-step explanation:

GIven : Linear correlation coefficient: r = 0.543

Sample size: n= 25

Significance levle: \alpha=0.05

Degree of freedom : n-2 = 25-2=23

Now, we check <em>r</em> critical value table for value with df = 23 and \alpha=0.05.

Critical value = ±0.396  [From <em>r</em> critical value table]

Since r = 0.543 > 0.396, that means there is significant linear correlation.

Hence,  <em>r</em> represents a significant linear correlation.

8 0
3 years ago
Convert 657 as binary form in computer language​
Monica [59]

Answer:

1010010001

Step-by-step explanation:

Keep dividing 657 by 2, and record the quotient and remainder

657

328,1

164,0

82,0

41,0

20,1

10,0

5,0

2,1

1,0

So chain the remainders from bottom up to get the binary number:

1010010001

Check:

1+16+128+512=657  checks.

5 0
3 years ago
Pla help pls : What is the first step to solving the following equation?<br> 5x – 11 = 42
kow [346]

Answer:

x = 10.6

Step-by-step explanation:

5x - 11 = 42

first +11 so,

5x = 53

then ÷5

x = 10.6

3 0
3 years ago
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