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SIZIF [17.4K]
3 years ago
13

What is the solution to the system of equations? -7x-2y+z=-2 6x-y-z=-18 5x+4y-z=18

Mathematics
1 answer:
irinina [24]3 years ago
5 0

Answer:

x = -1, y = 7 , z = 5.

Step-by-step explanation:

-7x - 2y + z = -2  .........(1)

6x -  y - z  =  -18........(2)

5x + 4y - z=  18..........(3)

Subtract equations (2) - (3):

x  - 5y = -36.........(4)

Add equations (1) and (2):

-x  - 3y = -20.......(5)

Adding (4) and (5):

-8y = -56

y = 7.

Substitute y = 7 into equation 4:

x - 5(7) = -36

x - 35 = -36

x = -1.

Substitute x = -1 and y = 7 in equation (1):

-7(-1) - 2(7) + z = -2

7 - 14 + z = -2

z = -2 - 7 + 14

z =  5.

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\large\begin{array}{l} \left\{\!\begin{array}{l} \mathsf{f(x)=x^2-6x+2}\\ \mathsf{g(x)=\sqrt{x}}\\ \end{array}\right. \end{array}


\large\begin{array}{l} \textsf{a) }\mathsf{(f\circ g)(x)}\\\\ =\mathsf{f\big[g(x)\big]}\\\\ =\mathsf{\big[g(x)\big]^2-6\cdot g(x)+2}\\\\ =\mathsf{\big[\sqrt{x}\big]^2-6\sqrt{x}+2}\\\\\\ \therefore~~\boxed{\begin{array}{c}\mathsf{(f\circ g)(x)=x-6\sqrt{x}+2} \end{array}}\qquad\checkmark \end{array}

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\large\begin{array}{l} \textsf{b) }\mathsf{(g\circ f)(-2)}\\\\ =\mathsf{g\big[f(-2)\big]}\\\\ =\mathsf{\sqrt{f(-2)}}\\\\ =\mathsf{\sqrt{(-2)^2-6\cdot (-2)+2}}\\\\ =\mathsf{\sqrt{4+12+2}}\\\\ =\mathsf{\sqrt{18}}\\\\ =\mathsf{\sqrt{3^2\cdot 2}}\\\\ =\mathsf{3\sqrt{2}}\\\\\\ \therefore~~\boxed{\begin{array}{c}\mathsf{(g\circ f)(-2)=3\sqrt{2}} \end{array}}\qquad\checkmark \end{array}

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If you're having problems understanding this answer, try seeing it through your browser: brainly.com/question/2181559


\large\textsf{I hope this helps. :-)}


Tags: <em>composite function composition evaluate algebra</em>

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