Chapter 4: Q. 345 (page 479)

In the following exercises, solve the systems of equations by elimination.
$\{\begin{cases} \frac{1}{3} x - \frac{1}{2} y = 1 \\ \frac{3}{4} x - y = \frac{5}{2} \end{cases}$

Short Answer

Expert verified

The solution for the system of linear equation is $(6, 2)$ .

Step by step solution

Step 1. Given information.

The system of linear equations,

$\{\begin{cases} \frac{1}{3} x - \frac{1}{2} y = 1 \\ \frac{3}{4} x - y = \frac{5}{2} \end{cases}$

Step 2. Calculating the value of x.

Now, we will make some changes in the equations to eliminate $y$ terms.

Multiplying the first equation with $2$ we get

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

Then the equations will be,

$\frac{2}{3} x - y = 2 \frac{3}{4} x - y = \frac{5}{2}$

Subtracting the above equations then

$\frac{2}{3} x - y = 2 - \frac{3}{4} x + y = - \frac{5}{2} (\frac{2}{3} - \frac{3}{4}) x = 2 - \frac{5}{2} \frac{- 1}{12} x = \frac{- 1}{2} x = 6$

Step 3. Calculating the value of y.

Substituting the value of $x$ in any equation.

$\frac{1}{3} (6) - \frac{1}{2} y = 1 2 - \frac{1}{2} y = 1 - \frac{1}{2} y = - 1 y = 2$

Step 4. Checking the result.

Substituting the value of $x$ and $y$ in the first equation then

$\frac{1}{3} x - \frac{1}{2} y = 1 \frac{1}{3} (6) - \frac{1}{2} (2) = 1 2 - 1 = 1 1 = 1$

Substituting the value of $x$ and $y$ in the second equation then

$\frac{3}{4} x - y = \frac{5}{2} \frac{3}{4} (6) - 2 = \frac{5}{2} \frac{9}{2} - 2 = \frac{5}{2} 9 - 4 = 5 5 = 5$

Hence, this is true.

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In the following exercises, solve the systems of equations by elimination.
$\{\begin{cases} \frac{1}{3} x - \frac{1}{2} y = 1 \\ \frac{3}{4} x - y = \frac{5}{2} \end{cases}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculating the value of x.

Step 3. Calculating the value of y.

Step 4. Checking the result.

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In the following exercises, solve the systems of equations by elimination. 13x-12y=134x-y=52

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculating the value of x.

Step 3. Calculating the value of y.

Step 4. Checking the result.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Applied Mathematics

Logic and Functions

Decision Maths

Statistics

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Study anywhere. Anytime. Across all devices.

In the following exercises, solve the systems of equations by elimination.
$\{\begin{cases} \frac{1}{3} x - \frac{1}{2} y = 1 \\ \frac{3}{4} x - y = \frac{5}{2} \end{cases}$