Q48. Determine the best method to sol... [FREE SOLUTION]

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Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 6: Q48. (page 391)

Determine the best method to solve each system of equations. Then solve the system.
$\begin{array}{l} 6 x + 5 y = 9 \\ 鈭� 2 x + 4 y = 14 \end{array}$

Short Answer

Expert verified

The best method to solve the system of equations is Elimination method.The solution of the system of equations is $(鈭� 1, 3)$ .

Step by step solution

Step 1. State the concept of substitution method and elimination method.

The substitution method is used to find the set of solutions for the given system of equations. It is the method in which one variable is first solved in the form of another variable.

So, the value of one variable in the form second variable is put on the second equation. It will give the solution of the one variable. And then solve it for another variable.

The elimination method is the method in which addition or subtraction method is used to get an equation in the one variable.

If the coefficients are opposite, use the addition and when the coefficients are same, use the subtraction.

Step 2. Add or subtract the equations to eliminate one variable.

The given system of equation is:

$6 x + 5 y = 9$ 鈥� (1)

$鈭� 2 x + 4 y = 14$ 鈥� (2)

Multiply equation (2) by 3.

role="math" localid="1647582191703" $\begin{array}{l} 3 (鈭� 2 x + 4 y) = 3 脳 (14) \\ 鈭� 6 x + 12 y = 42 鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌�....鈥� (3) \end{array}$

Note that both the equations (1) and (3) have $6 x$ in opposite signs, therefore, variable $x$ can be eliminated if both equations are added.

$\begin{array}{l} 鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌� 6 x + 5 y = 9 \\ \underset{炉}{(+) 鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌� 鈭� 6 x + 12 y = 42} \\ 鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆€夆€� 17 y = 51 Dividebothsidesby17 \\ 鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆€夆€夆€夆€夆€夆€� y = 3 \end{array}$

Step 3. Solve for x.

Substitute 3 for y into the equation (1) and solve for $x$ . $\begin{matrix} 6 x + 5 y = 9 \\ 6 x + 5 (3) 鈭� 15 = 9 鈭� 15 \\ 6 x = 鈭� 6 \\ x = 鈭� 1 \end{matrix}$

The solution is $(鈭� 1, 3)$ .

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91影视

Determine the best method to solve each system of equations. Then solve the system.
$\begin{array}{l} 6 x + 5 y = 9 \\ 鈭� 2 x + 4 y = 14 \end{array}$

Short Answer

Step by step solution

Step 1. State the concept of substitution method and elimination method.

Step 2. Add or subtract the equations to eliminate one variable.

Step 3. Solve for x.

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91影视

Determine the best method to solve each system of equations. Then solve the system.6x+5y=9鈭�2x+4y=14

Short Answer

Step by step solution

Step 1. State the concept of substitution method and elimination method.

Step 2. Add or subtract the equations to eliminate one variable.

Step 3. Solve for x.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Logic and Functions

Probability and Statistics

Discrete Mathematics

Calculus

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Determine the best method to solve each system of equations. Then solve the system.
$\begin{array}{l} 6 x + 5 y = 9 \\ 鈭� 2 x + 4 y = 14 \end{array}$