Chapter 5: Q.127 (page 626)

In the following exercises, solve the systems of equations by elimination.
$\{\begin{cases} - 3 x + y = - 9 \\ x - 2 y = - 12 \end{cases}$

Short Answer

Expert verified

The solution of the system is $(x, y) = (6, 9) .$

Step by step solution

Step 1. Given information

The given system is $\{\begin{cases} - 3 x + y = - 9 \\ x - 2 y = - 12 \end{cases}$

Step 2. solve for y

$\{\begin{cases} - 3 x + y = - 9 \\ x - 2 y = - 12 \end{cases} Given \{\begin{cases} - 3 x + y = - 9 \\ 3 (x - 2 y) = 3 (- 12) \end{cases} multiplysecondequationwith3 \{\begin{cases} - 3 x + y = - 9 \\ 3 x - 6 y = - 36 \end{cases} simplify$

Add both equations

$\begin{array}{l} - 3 x + y = - 9 \\ 3 x - 6 y = - 36 \end{array} - 5 y = - 45 y = \frac{- 45}{- 5} y = 9$

Step 3. solve for x

$\begin{array}{l} - 3 x + y = - 9 firstequation \\ - 3 x + 9 = - 9 use y = 9 \\ - 3 x = - 9 - 9 solvefor x \\ - 3 x = - 18 \\ x = \frac{- 18}{- 3} \\ x = 6 \end{array}$

Hence, $(x, y) = (6, 9)$

Step 4. Verify the solution

$\begin{array}{l} - 3 x + y = - 9 \Rightarrow - 3 (6) + 9 = - 9 \\ - 18 + 9 = - 9 \\ - 9 = - 9 true \\ x - 2 y = - 12 \Rightarrow 6 - 2 (9) = - 12 \\ 6 - 18 = - 12 \\ - 12 = - 12 true \end{array}$

Both equations are true.

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In the following exercises, solve the systems of equations by elimination.
$\{\begin{cases} - 3 x + y = - 9 \\ x - 2 y = - 12 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. solve for y

Step 3. solve for x

Step 4. Verify the solution

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In the following exercises, solve the systems of equations by elimination.-3x+y=-9x-2y=-12

Short Answer

Step by step solution

Step 1. Given information

Step 2. solve for y

Step 3. solve for x

Step 4. Verify the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Statistics

Geometry

Logic and Functions

Theoretical and Mathematical Physics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve the systems of equations by elimination.
$\{\begin{cases} - 3 x + y = - 9 \\ x - 2 y = - 12 \end{cases}$