Q34. Use elimination to solve each sy... [FREE SOLUTION]

91影视

Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 6: Q34. (page 390)

Use elimination to solve each system of equations.
$\begin{array}{l} x + y = 4 \\ 鈭� 2 x + 3 y = 7 \end{array}$

Short Answer

Expert verified

The solution of the system of equations is $(1, 3)$ .

Step by step solution

Step 1. State the concept of elimination method to solve system of equations.

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:

$x + y = 4$ 鈥� (1)

$鈭� 2 x + 3 y = 7$ 鈥� (2)

Multiply equation (1) by 2.

$\begin{array}{l} 2 脳 (x + y) = 2 脳 4 \\ 2 x + 2 y = 8 鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌� (3) \end{array}$

Note that both the equations (2) and (3) havelocalid="1647514787891" $2 x$ in opposite signs, therefore, variablelocalid="1647514783732" $x$ can be eliminated if both equations are added.

localid="1650702948718" $\begin{array}{l} 鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌� 鈭� 2 x + 3 y = 7 \\ \underset{炉}{(+) 鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌� 2 x + 2 y = 8} \\ 鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆€夆€夆€夆€夆€夆€夆€夆€夆€夆€� 5 y = 15 Dividebothsidesby5 \\ 鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆€夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆€� y = 3 \end{array}$

Step 3. Solve for x.

Substitute 3 for $y$ into the equation (1) and solve for $x$ .

$\begin{matrix} x + y = 4 \\ x + 3 鈭� 3 = 4 鈭� 3 \\ x = 1 \end{matrix}$

The solution islocalid="1647514838622" $(1, 3)$ .

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91影视

Use elimination to solve each system of equations.
$\begin{array}{l} x + y = 4 \\ 鈭� 2 x + 3 y = 7 \end{array}$

Short Answer

Step by step solution

Step 1. State the concept of elimination method to solve system of equations.

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

Step 3. Solve for x.

One App. One Place for Learning.

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91影视

Use elimination to solve each system of equations.x+y=4鈭�2x+3y=7

Short Answer

Step by step solution

Step 1. State the concept of elimination method to solve system of equations.

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

Decision Maths

Logic and Functions

Geometry

Theoretical and Mathematical Physics

Probability and Statistics

Calculus

Study anywhere. Anytime. Across all devices.

Use elimination to solve each system of equations.
$\begin{array}{l} x + y = 4 \\ 鈭� 2 x + 3 y = 7 \end{array}$