Chapter 3: Q49. (page 135)

Solve each system of equations by using either substitution or elimination
49. $\begin{matrix} 6 x + y = 15 \\ x - 4 y = - 10 \end{matrix}$

Short Answer

Expert verified

The solution of the system of equations is $(x, y) = (2, 3)$ .

Step by step solution

– Apply elimination method to solve the system of equations.

Elimination method enables us to eliminate or get rid of one of the variable, so we can solve a more simplified equation.

– Evaluate the system of equations

Given system of equations:

\begin{matrix} 6 x + y = 15 \\ x - 4 y = - 10 \end{matrix}

Multiply the first equation, $6 x + y = 15$ by 4 and add the new resultant equation to the equation is $x - 4 y = - 10$ .

$\begin{array}{l} \underline{\begin{matrix} 6 x + y = 15 \\ x - 4 y = - 10 \end{matrix}} \begin{matrix} multiplyby4 \to \end{matrix} \underline{\begin{matrix} 24 x + 4 y = 60 \\ x - 4 y = - 10 \end{matrix}} \\ 25 x + 0 y = 50 \end{array}$

Solve the equation $25 x = 50$ for x:

$\begin{matrix} 25 x = 50 \\ \frac{25 x}{25} = \frac{50}{25} dividebothsidesby25 \\ x = 2 \end{matrix}$

– Find the value of y

Substitute $x = 2$ in $6 x + y = 15$ and solve for $y :$

$\begin{matrix} 6 x + y = 15 \\ 6 (2) + y = 15 substitute2for x \\ 12 + y = 15 simplify \\ y = 3 subtract12frombothsides \end{matrix}$

So, the solution of the given system is $(x, y) = (2, 3)$ .

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Solve each system of equations by using either substitution or elimination
49. $\begin{matrix} 6 x + y = 15 \\ x - 4 y = - 10 \end{matrix}$

Short Answer

Step by step solution

– Apply elimination method to solve the system of equations.

– Evaluate the system of equations

– Find the value of y

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Solve each system of equations by using either substitution or elimination49.6x+y=15x−4y=−10

Short Answer

Step by step solution

– Apply elimination method to solve the system of equations.

– Evaluate the system of equations

– Find the value of y

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Theoretical and Mathematical Physics

Probability and Statistics

Discrete Mathematics

Mechanics Maths

Statistics

Study anywhere. Anytime. Across all devices.

Solve each system of equations by using either substitution or elimination
49. $\begin{matrix} 6 x + y = 15 \\ x - 4 y = - 10 \end{matrix}$