Q15. Solve each system of equations聽... [FREE SOLUTION]

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Chapter 3: Q15. (page 142)

Solve each system of equations
$\begin{array}{l} 8 x 鈭� 6 z = 38 \\ 2 x 鈭� 5 y + 3 z = 5 \\ x + 10 y 鈭� 4 z = 8 \end{array}$

Short Answer

Expert verified

The solution set of the given system of equations is $(4, 0, - 1)$ .

Step by step solution

– Use the elimination method to get the system of equations in two variables.

Multiply the equation $2 x - 5 y + 3 z = 5$ by $2$ and add the new resultant equation to $x + 10 y - 4 z = 8$ .

$\begin{array}{l} \underline{\begin{array}{l} 2 x 鈭� 5 y + 3 z = 5 \\ x + 10 y 鈭� 4 z = 8 \end{array}} 鈥夆赌夆赌夆赌� \begin{matrix} multiplyby2 \end{matrix} 鈥夆赌� \underline{\begin{array}{l} 4 x 鈭� 10 y + 6 z = 10 \\ 鈥夆赌� x + 10 y 鈭� 4 z = 鈥夆赌� 8 \end{array}} \\ 鈥夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌� 5 x + 鈥夆赌夆赌夆赌� 0 + 2 z = 18 \end{array}$

So, the resultant equation is $5 x + 2 z = 18$ .

– Use the elimination method to solve the system of two equations.

Multiply $5 x + 2 z = 18$ by 3 and add the new resultant equation to $8 x - 6 z = 38$ .

$\begin{array}{l} \underline{\begin{array}{l} 5 x + 2 z = 18 \\ 8 x 鈭� 6 z = 38 \end{array}} 鈥夆赌夆赌夆赌� \begin{matrix} multiplyby3 \end{matrix} 鈥夆赌� \underline{\begin{array}{l} 15 x + 6 z = 54 \\ 鈥� 8 x 鈭� 6 z = 38 \end{array}} \\ 鈥夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌� 23 x + 鈥夆赌� 0 = 92 \end{array}$

Solve for : $\begin{array}{l} 23 x = 92 \\ \frac{23 x}{23} = \frac{92}{23} 鈥夆赌夆赌夆赌夆€夆赌塂ividebothsidesby23 \\ x = 4 \end{array}$

– Find the values of yand z.

Substitute $x = 4 i n 5 x + 2 z = 18$ and find the value of $z$ .

$\begin{array}{l} 5 x + 2 z = 18 \\ 5 (4) + 2 z = 18 鈥夆赌夆赌夆赌塖ubstitute4for x \\ 20 + 2 z = 18 鈥夆赌夆赌夆赌夆€夆赌夆€塖implify \\ 2 z = 鈭� 2 鈥夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆€塖ubtract20frombothsides \\ z = 鈭� 1 鈥夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€塂ividebothsidesby2 \end{array}$

Substitute $x = 4, z = - 1 i n 2 x - 5 y + 3 z = 5$ and find the value of $y$

$\begin{array}{l} 2 x 鈭� 5 y + 3 z = 5 \\ 2 (4) 鈭� 5 y + 3 (鈭� 1) = 5 鈥夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌塻ubstitute4for x, 鈭� 1 for z \\ 8 鈭� 5 y 鈭� 3 = 5 鈥夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌塻implify \\ 5 鈭� 5 y = 5 鈥夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌塻implify \\ 鈭� 5 y = 0 鈥夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌塻ubtract5frombothsides \\ y = 0 鈥夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌塪ividebothsidesby 鈭� 5 \end{array}$

Hence, the solution of the given system of equations is $(x, y, z) = (4, 0, - 1)$ .

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91影视

Solve each system of equations
$\begin{array}{l} 8 x 鈭� 6 z = 38 \\ 2 x 鈭� 5 y + 3 z = 5 \\ x + 10 y 鈭� 4 z = 8 \end{array}$

Short Answer

Step by step solution

– Use the elimination method to get the system of equations in two variables.

– Use the elimination method to solve the system of two equations.

– Find the values of yand z.

One App. One Place for Learning.

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91影视

Solve each system of equations8x鈭�6z=382x鈭�5y+3z=5x+10y鈭�4z=8

Short Answer

Step by step solution

– Use the elimination method to get the system of equations in two variables.

– Use the elimination method to solve the system of two equations.

– Find the values of yand z.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Decision Maths

Applied Mathematics

Geometry

Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

Solve each system of equations
$\begin{array}{l} 8 x 鈭� 6 z = 38 \\ 2 x 鈭� 5 y + 3 z = 5 \\ x + 10 y 鈭� 4 z = 8 \end{array}$