Chapter 6: Q29. (page 390)

Use elimination to solve each system of equations.
$\begin{array}{l} 6 x + y = 9 \\ - 6 x + 3 y = 15 \end{array}$

Short Answer

Expert verified

The solution of the system of equations is $(\frac{1}{2}, 6)$ .

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:

$6 x + y = 9$ … (1)

$- 6 x + 3 y = 15$ … (2)

Note that both the equations havelocalid="1647511662747" $6 x$ in opposite signs, therefore, variablelocalid="1647511671435" $x$ can be eliminated if both equations are added. $\begin{array}{l} 6 x + y = 9 \\ \underline{(+) - 6 x + 3 y = 15} \\ 4 y = 24 Dividebothsidesby4 \\ y = 6 \end{array}$

Step 3. Solve for x.

Substitute 6 for $y$ into the equation (1) and solve for $x$ .

$\begin{matrix} 6 x + y = 9 \\ 6 x + 6 - 6 = 9 - 6 \\ 6 x = 3 \\ x = \frac{1}{2} \end{matrix}$

The solution is $(\frac{1}{2}, 6)$ .

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Use elimination to solve each system of equations.
$\begin{array}{l} 6 x + y = 9 \\ - 6 x + 3 y = 15 \end{array}$

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.

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Use elimination to solve each system of equations.6x+y=9−6x+3y=15

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

Pure Maths

Logic and Functions

Applied Mathematics

Discrete Mathematics

Calculus

Geometry

Study anywhere. Anytime. Across all devices.

Use elimination to solve each system of equations.
$\begin{array}{l} 6 x + y = 9 \\ - 6 x + 3 y = 15 \end{array}$