Chapter 4: Q. 4.21 (page 382)

Solve each system 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 of the system are $x = 6 y = 2$ .

Step by step solution

Given information.

The given system of equations is,

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

Isolation of variable

The equation is $\frac{1}{3} x - \frac{1}{2} y = 1$ . Isolating the variable. We get $x = 3 + \frac{3}{2} y$ .

Now substituting the value of $x$ in the other equation, we get

$[\frac{3}{4} (3 + \frac{3}{2} y) - y = \frac{5}{2}]$ .

Isolating and solving further

Further solving, we get $[\frac{18 + y}{8} = \frac{5}{2}]$ , isolating $y$ , we get

$y = 2$

Substitute, $y = 2$ , we get

$x = 3 + \frac{3}{2} \cdot 2$

$x = 6$

So the values are $x = 6 y = 2$

Checking the value

Substituting, we get

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

Checking for another value

Checking for another value, we get

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

So the value is correct

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Solve each system 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

Given information.

Isolation of variable

Isolating and solving further

Checking the value

Checking for another value

One App. One Place for Learning.

Most popular questions from this chapter

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Solve each system by elimination: 13x-12y=134x-y=52

Short Answer

Step by step solution

Given information.

Isolation of variable

Isolating and solving further

Checking the value

Checking for another value

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Decision Maths

Theoretical and Mathematical Physics

Mechanics Maths

Probability and Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Solve each system by elimination: $\{\begin{cases} \frac{1}{3} x - \frac{1}{2} y = 1 \\ \frac{3}{4} x - y = \frac{5}{2} \end{cases}$