~Giving brainliest!~ (im really desperate right now and very overwhelmed so im asking ANYONE to help me answer this! thank u.

Solve the system of linear equations.

sweet-ann [11.9K]

Answer:

dependent system
x = 2 -a
y = 1 +a
z = a

Step-by-step explanation:

Let's solve this by eliminating z, then we'll go from there.

Add 6 times the second equation to the first.

(3x -3y +6z) +6(x +2y -z) = (3) +6(4)

9x +9y = 27 . . . simplify

x + y = 3 . . . . . . divide by 9 [eq4]

Add 13 times the second equation to the third.

(5x -8y +13z) +13(x +2y -z) = (2) +13(4)

18x +18y = 54

x + y = 3 . . . . . . divide by 18 [eq5]

Equations [eq4] and [eq5] are identical. This tells us the system is dependent, and has an infinite number of solutions. We can find them in terms of z:

y = 3 -x . . . . solve eq5 for y

x +2(3 -x) -z = 4 . . . . substitute into the second equation

-x +6 -z = 4

x = 2 - z . . . . . . add x-4

y = 3 -(2 -z)

y = z +1

So far, we have written the solutions in terms of z. If we use the parameter "a", we can write the solutions as ...

x = 2 -a

y = 1 +a

z = a

_____

<em>Check</em>

First equation:

3(2-a) -3(a+1) +6a = 3

6 -3a -3a -3 +6a = 3 . . . true

Second equation:

(2-a) +2(a+1) -a = 4

2 -a +2a +2 -a = 4 . . . true

Third equation:

5(2-a) -8(a+1) +13a = 2

10 -5a -8a -8 +13a = 2 . . . true

Our solution checks algebraically.

6 0

3 years ago

What is the gradient of the graph shown below. Give answer in simplest for

katovenus [111]

Answer:

1

Step-by-step explanation:

Choose two points on the line: (-5, 0) and (0, 5)

Let the first point $(x_1,y_1)$ = (-5, 0)

Let the second point $(x_2,y_2)$ = (0, 5)

Use the gradient formula:

$\textsf{gradient}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{5-0}{0-(-5)}=1$

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If you want to find the equation of the line, use the point-gradient form of a linear equation: $y-y_1=m(x-x_1)$

(where $m$ is the gradient and $(x_1,y_1)$ is a point on the line)

Substituting the values into the formula:

$\implies y-0=1(x-(-5))$

$\implies y-0=x+5$

$\implies y=x+5$

Therefore, the equation of the line is y = x + 5

3 0

2 years ago

Jackie can type 230 words in 4 minutes. Howard can type 296 words in 5 minu

inna [77]

Answer:

A

B

D

Step-by-step explanation:

A 230 divided by 4 is 57.5 which makes A a true statement.

B 296 divided by 5 is 59.2 which makes B a true statement .

D 296 - 230 =66

66 - 57.5 = 8.5

Which makes D a true statement by a margin of 8.5 words.

5 0

3 years ago

I'll give brainliest to whoever answers this question first with correct steps that I can understand

Kazeer [188]

Answer:

You multiply 64 and 4 or 32 by 8 and both should equal 256 grams .-.

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

If the discriminant of a<br> quadratic equation is equal to -8, which statement describes the roots?

lana66690 [7]

Answer:

Since -8<0 then the roots α and β of the quadratic equation ax^2 + bx + c = 0 are unequal and imaginary: α and β are a pair of the complex conjugates.

8 0

3 years ago