Mathematics, 24.03.2020 01:34 misrachel03

Determine the values of a for which the system has no solutions, exactly one solution, or infinitely many solutions. x + 2y + z = 2, 2x - 2y + 3z = 1, x + 2y - (a2 - 3)z = a

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Answer from: mfkinnatz

a) If $2-a^{2}=0$ and $a-2\neq 0$ . The system has no solution

b) If $2-a^{2}\neq 0$ and a different to 2, we have a unique solution.

c) If $2-a^{2}=0$ and a-2=0 we have infinitely solutions.

Step-by-step explanation:

We need to rewrite the third equation in terms of a and z to solve this.

Let's start solving the first equation:

x+2y+z=2 (1)

If we subtract z in both side of this equation we will have:

x+2y=2-z (2)

Now we can put the equation 2 into the last equation:

$x+2y-(a^{2}-3)z=a$

$2-z-(a^{2}-3)z=a$ (3)

Simplifying the equation 3 we have:

$z(2-a^{2})=a-2$ (4)

Now we can analyzes the equation 4 for each case:

a) If $2-a^{2}=0$ and $a-2\neq 0$ . The system has no solution

b) If $2-a^{2}\neq 0$ and a different to 2, we have a unique solution.

c) If $2-a^{2}=0$ and a-2=0 we have infinitely solutions.

I hope it helps you!

Answer from: Quest

a. we have two

lines: y = 4-x and

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b. 4-x = 8-x^-1

x 4-x 8-x^-1

-3 7

8.33

-2 6 8.5

-1 5 9

0 4

1 3

2 2

7.5

3 1 7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:

x=-4.236

y = 4-x = 4 – (-4.236)

= 8.236

y = 8-x^-1 = .236)^-1

= 8.236

x=0.236

y = 4-x = 4 – (0.236) = 3.764

y = 8-x^-1 = 8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c. to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x and y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines. the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!

Answer from: Quest

yes the data was not prsented

step-by-step explanation:

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Determine the values of a for which the system has no solutions, exactly one solution, or infinitely...

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