Chapter 4: Q38. (page 158)

Solve each system of equations.
$\begin{matrix} 3 a + 2 b = 27 \\ 5 a - 7 b + c = 5 \\ - 2 a + 10 b + 5 c = - 29 \end{matrix}$

Short Answer

Expert verified

The solution of given system of equation is $(7, 3, - 9)$ .

Step by step solution

– Description of step.

Multiply $5 a - 7 b + c = 5$ by 5 and subtract $- 2 a + 10 b + 5 c = - 29$ from the obtained equation.

\begin{matrix} 25 a - 35 b + 5 c - (- 2 a + 10 b + 5 c) = 25 - (- 29) \\ 25 a - 35 b + 5 c + 2 a - 10 b - 5 c = 54 \\ 25 a - 35 b + 2 a - 10 b = 54 \\ 27 a - 45 b = 54 \end{matrix}

– Description of step.

Multiply $3 a + 2 b = 27$ by 9 and subtract $27 a - 45 b = 54$ from the obtained equation.

\begin{matrix} 27 a + 18 b - (27 a - 45 b) = 243 - 54 \\ 27 a + 18 b - 27 a + 45 b = 189 \\ \frac{63 b}{63} = \frac{189}{63} \\ b = 3 \end{matrix}

– Description of step.

Substitute 3 for $b$ into $3 a + 2 b = 27$ and simplify to obtain the value of $a$ .

\begin{matrix} 3 a + 2 (3) = 27 \\ 3 a + 6 = 27 \\ \frac{3 a}{3} = \frac{21}{3} \\ a = 7 \end{matrix}

– Description of step.

Substitute 3 for $b$ and 7 for $a$ into $5 a - 7 b + c = 5$ and simplify to obtain the value of $c$ .

\begin{matrix} 5 (7) - 7 (3) + c = 5 \\ 35 - 21 + c = 5 \\ 14 + c = 5 \\ c = - 9 \end{matrix}

Therefore, the solution of given system of equation is $(7, 3, - 9)$ .

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Solve each system of equations.
$\begin{matrix} 3 a + 2 b = 27 \\ 5 a - 7 b + c = 5 \\ - 2 a + 10 b + 5 c = - 29 \end{matrix}$

Short Answer

Step by step solution

– Description of step.

– Description of step.

– Description of step.

– Description of step.

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Solve each system of equations.3a+2b=275a-7b+c=5-2a+10b+5c=-29

Short Answer

Step by step solution

– Description of step.

– Description of step.

– Description of step.

– Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Geometry

Applied Mathematics

Pure Maths

Discrete Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

Solve each system of equations.
$\begin{matrix} 3 a + 2 b = 27 \\ 5 a - 7 b + c = 5 \\ - 2 a + 10 b + 5 c = - 29 \end{matrix}$