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Sergeeva-Olga [200]
2 years ago
7

Solve the system of equations: x+3y-z=9 2x+9y+4z=12 x+4y+z=7

Mathematics
1 answer:
Lelechka [254]2 years ago
7 0

[i] … … … x + 3y - z = 9

[ii] … … … 2x + 9y + 4z = 12

[iii] … … … x + 4y + z = 7

Eliminate z by combining …

• … 4 times equation [i] and equation [ii] :

4 (x + 3y - z) + (2x + 9y + 4z) = 4•9 + 12

(4x + 12y - 4z) + (2x + 9y + 4z) = 36 + 12

6x + 21y = 48

2x + 7y = 16

• … equation [i] and equation [iii] :

(x + 3y - z) + (x + 4y + z) = 9 + 7

2x + 7y = 16

Since we ended up with 2 copies of the same equation, we have infinitely many solutions for x, y, and z. That is, we have infinitely many choices for x and y that satisfy 2x + 7y = 16, and consequently infinitely many choices for z to satisfy any of the 3 original equations.

We can parameterize the solution by letting, for instance, x = t; then the solution set is

x = t

2x + 7y = 16   ⇒   y = (16 - 2t)/7

x + 3y - z = 9   ⇒   z = t + 3 (16 - 2t)/7 - 9   ⇒   z = (t - 15)/7

where t is any real number.

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Read 2 more answers
Please give me the correct answer ​
Ganezh [65]

Answer:

PQ = 5 units

QR = 8 units

Step-by-step explanation:

Given

P(-3, 3)

Q(2, 3)

R(2, -5)

To determine

The length of the segment PQ

The length of the segment QR

Determining the length of the segment PQ

From the figure, it is clear that P(-3, 3) and Q(2, 3) lies on a horizontal line. So, all we need is to count the horizontal units between them to determine the length of the segments P and Q.

so

P(-3, 3), Q(2, 3)

PQ = 2 - (-3)

PQ = 2+3

PQ = 5 units

Therefore, the length of the segment PQ = 5 units

Determining the length of the segment QR

Q(2, 3), R(2, -5)

(x₁, y₁) = (2, 3)

(x₂, y₂) = (2, -5)

The length between the segment QR is:

l=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}

  =\sqrt{\left(2-2\right)^2+\left(-5-3\right)^2}

  =\sqrt{0+8^2}

  =\sqrt{8^2}

Apply radical rule: \sqrt[n]{a^n}=a,\:\quad \mathrm{\:assuming\:}a\ge 0

  =8

Therefore, the length between the segment QR is: 8 units

Summary:

PQ = 5 units

QR = 8 units

8 0
3 years ago
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