Chapter 4: Q 56 (page 386)

In the following exercise, solve the systems of equations by elimination.
$\{\begin{cases} \frac{1}{3} x - y = - 3 \\ x + \frac{5}{2} y = 2 \end{cases}$

Short Answer

Expert verified

The solution is $(- 3, 2)$ .

Step by step solution

Step 1. Given information

The given equations are

$\frac{1}{3} x - y = - 3$

$x + \frac{5}{2} y = 2$

Step 2. Calculating the value of y

To calculate the value of $y$ we have to eliminate the $x' s$ term.

Let us do some changes through which we can easily eliminate $x$ .

1) multiply the first equation by $- 3$

$- 3 (\frac{1}{3} x - y = - 3)$

$- x + 3 y = 9$

now, the new equations are

$- x + 3 y = 9 x + \frac{5}{2} y = 2$

just add the equations

$- x + 3 y = 9 x + \frac{5}{2} y = 2 \frac{11}{2} y = 11$

$y = 2$

the value of $y$ =2

Step 3. Calculating the value of x

As we have the value of $y$ , we can substitute it in any equation and hence calculate the value of $x$ .

let us take the first equation

$\frac{1}{3} x - y = - 3$

put $y$ =2

$\frac{1}{3} x - 2 = - 3 \frac{1}{3} x = - 1 x = - 3$

the value of x is $- 3$ .

Step 4. Checking the solution

Checking the solution by putting the value of $x, y$ in the equation, we get

$\frac{1}{3} x - y = - 3 \frac{1}{3} (- 3) - 2 = - 3 - 1 - 2 = - 3 - 3 = - 3 x + \frac{5}{2} y = 2 - 3 + \frac{5}{2} (2) = 2 - 3 + 5 = 2 2 = 2$

This is true, hence the solution is correct.

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In the following exercise, solve the systems of equations by elimination.
$\{\begin{cases} \frac{1}{3} x - y = - 3 \\ x + \frac{5}{2} y = 2 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculating the value of y

Step 3. Calculating the value of x

Step 4. Checking the solution

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In the following exercise, solve the systems of equations by elimination.13x-y=-3x+52y=2

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculating the value of y

Step 3. Calculating the value of x

Step 4. Checking the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

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Study anywhere. Anytime. Across all devices.

In the following exercise, solve the systems of equations by elimination.
$\{\begin{cases} \frac{1}{3} x - y = - 3 \\ x + \frac{5}{2} y = 2 \end{cases}$