Q50. Solve each system of equations b... [FREE SOLUTION]

Chapter 3: Q50. (page 135)

Solve each system of equations by using either substitution or elimination 50 $\begin{matrix} 3 x + 8 y = 23 \\ 5 x 鈭� y = 24 \end{matrix}$

Short Answer

Expert verified

The solution of the system of equations is . $(x, y) = (5, 1)$

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: $\begin{matrix} 3 x + 8 y = 23 \\ 5 x 鈭� y = 24 \end{matrix}$

Multiply the second equation, $5 x - y = 24$ by 8 and add the new resultant equation to the equation is $3 x + 8 y = 23$

$\begin{array}{l} \underline{\begin{matrix} 3 x + 8 y = 23 \\ 5 x 鈭� y = 24 \end{matrix}} 鈥夆赌� \begin{matrix} multiplyby8 鈫� \end{matrix} 鈥夆赌夆€夆赌� \underline{\begin{matrix} 3 x + 8 y = 鈥夆赌夆€� 23 \\ 40 x 鈭� 8 y = 192 \end{matrix}} \\ 鈥夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌夆€� 43 x + 0 y = 鈥� 215 \end{array}$

Solve the equation $43 x = 215$ for $x$ $\begin{matrix} 43 x = 215 \\ \frac{43 x}{43} = \frac{215}{43} 鈥夆赌夆€夆赌夆€夆赌塪ividebothsidesby43 \\ x = 5 \end{matrix}$ :

– Find the value of y

Substitute $x = 5$ in $5 x - y = 24$ and solve for $y :$

$\begin{matrix} 5 x 鈭� y = 24 \\ 5 (5) 鈭� y = 24 鈥夆赌夆€夆赌夆€夆赌夆€夆赌夆€塻ubstitute5for x \\ 25 鈭� y = 24 鈥夆赌夆€夆赌夆€夆赌夆€夆赌夆€塻implify \\ 鈭� y = 鈭� 1 鈥夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌塻ubtract25frombothsides \\ y = 1 dividebothsidesby 鈭� 1 \end{matrix}$

So, the solution of the given system is . $(x, y) = (5, 1)$

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Solve each system of equations by using either substitution or elimination 50 $\begin{matrix} 3 x + 8 y = 23 \\ 5 x 鈭� y = 24 \end{matrix}$

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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91影视

Solve each system of equations by using either substitution or elimination 503x+8y=235x鈭�y=24

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

Decision Maths

Pure Maths

Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Solve each system of equations by using either substitution or elimination 50 $\begin{matrix} 3 x + 8 y = 23 \\ 5 x 鈭� y = 24 \end{matrix}$