Chapter 5: Q.128 (page 626)

In the following exercises, solve the systems of equations by elimination.
$\{\begin{cases} 6 x - 5 y = - 1 \\ 2 x + y = 13 \end{cases}$

Short Answer

Expert verified

The solution of the system is $(x, y) = (4, 5) .$

Step by step solution

Step 1. Given information

The given system is $\{\begin{cases} 6 x - 5 y = - 1 \\ 2 x + y = 13 \end{cases}$

Step 2. solve for x

$\{\begin{cases} 6 x - 5 y = - 1 \\ 2 x + y = 13 \end{cases} G i v e n \{\begin{cases} 6 x - 5 y = - 1 \\ 5 (2 x + y) = 5 (13) Multiplyonbothsideswith5 \end{cases} \{\begin{cases} 6 x - 5 y = - 1 \\ 10 x + 5 y = 65 \end{cases} Simplify$

Add both equations

$\begin{array}{l} 6 x - 5 y = - 1 \\ 10 x + 5 y = 65 \end{array} 16 x = 64 x = \frac{64}{16} x = 4$

Step 3. solve for y

$\begin{array}{l} 6 x - 5 y = - 1 firstequation \\ 6 (4) - 5 y = - 1 use x = 4 \\ 24 - 5 y = - 1 solvefor y \\ 5 y = 24 + 1 \\ 5 y = 25 \\ y = \frac{25}{5} \\ y = 5 \end{array}$

Step 4. Verify the solution

$\begin{array}{l} 6 x - 5 y = - 1 \Rightarrow 6 (4) - 5 (5) = - 1 \\ 24 - 25 = - 1 \\ - 1 = - 1 true \\ 2 x + y = 13 \Rightarrow 2 (4) + 5 = 13 \\ 8 + 5 = 13 \\ 13 = 13 true \end{array}$

Both equations are true.

Hence, the solution is $(x, y) = (4, 5) .$

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In the following exercises, solve the systems of equations by elimination.
$\{\begin{cases} 6 x - 5 y = - 1 \\ 2 x + y = 13 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. solve for x

Step 3. solve for y

Step 4. Verify the solution

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In the following exercises, solve the systems of equations by elimination.6x-5y=-12x+y=13

Short Answer

Step by step solution

Step 1. Given information

Step 2. solve for x

Step 3. solve for y

Step 4. Verify the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Theoretical and Mathematical Physics

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In the following exercises, solve the systems of equations by elimination.
$\{\begin{cases} 6 x - 5 y = - 1 \\ 2 x + y = 13 \end{cases}$