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4 years ago

Solve the system of equations. 4x+2y+5z=8 5x+3y+4z=9 6x+3y+3z=3

Mathematics

1 answer:

Alchen [17]4 years ago

3 0

Answer:

x = -4, y = 7, z = 2.

Step-by-step explanation:

4x + 2y + 5z = 8......(1)

5x + 3y + 4z = 9......(2)

6x + 3y + 3z = 3......(3)

Subtract: equation (2) - equation (3):

-x + z = 6 ........(4)

Multiply (1) by 3 and (2) by 2:

12x + 6y + 15z = 24 .........(5)

10x + 6y + 8z = 18 ...........(6)

Subtract: (5) - (6):

2x + 7z = 6..............(7)

Multiply equation (4) by 2:

- 2x + 2z = 12.........(8)

Add (7) + (8):

9z = 18 , so z = 2.

Substitute for z in equation (4)

-x + 2 = 6

-x = 4 so x = -4.

Now find y by substituting in equation (1):

4(-4) + 2y + 5(2) = 8

2y = 8 + 16 - 10 = 14

y = 7.

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Step-by-step explanation:

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shepuryov [24]

Given:

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To solve this question, follow the steps below.

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You can choose 2 points from the table.

Let's choose (14, 8.96) and (16, 10.24).

Step 02: Substitute one point in the general equation.

Given the general equation:

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Substituting the first point.

$\begin{gathered} 8.96=14m+b \\ 8.96-14m=b \\ b=8.96-14m \end{gathered}$

Isolating b by subtracting 8.96 m from both sides:

$\begin{gathered} 14-8.96m=8.96m+b-8.96m \\ 14-8.96m=b \\ b=14-8.96m \end{gathered}$

Step 03: Substitute b in the general equation.

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Step 04: Substitute the second point in the equation above.

$\begin{gathered} c=ms+8.96-14m \\ 10.24=16m+8.96-14m \\ 10.24=2m+8.96 \end{gathered}$

Step 05: Solve the equation above for m.

To do it, first, subtract 8.96 from both sides.

$\begin{gathered} 10.24-8.96=2m+8.96-8.96 \\ 1.28=2m \end{gathered}$

Now, divide both sides by 2.

$\begin{gathered} \frac{1.28}{2}=\frac{2}{2}m \\ m=0.64 \end{gathered}$

Step 06: Substitute m in the equation from step 02 to find b.

$\begin{gathered} b=8.96-14m \\ b=8.96-14\cdot0.64 \\ b=8.96-8.96 \\ b=0 \end{gathered}$

Step 07: Write the equation.

$\begin{gathered} c=0.64s+0 \\ c=0.64s \end{gathered}$

Answer:

c = 0.64s

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