Chapter 4: Q. 4.22 (page 383)

Solve each system by elimination: $\{\begin{cases} x + \frac{3}{5} y = - \frac{1}{5} \\ - \frac{1}{2} x - \frac{2}{3} y = \frac{5}{6} \end{cases}$

Short Answer

Expert verified

The value of $x, y$ are $1, - 2$ respectively

Step by step solution

Given information

Given the system of equations $\{\begin{cases} x + \frac{3}{5} y = - \frac{1}{5} \\ - \frac{1}{2} x - \frac{2}{3} y = \frac{5}{6} \end{cases}$

Isolate the value of x

The value on isolating $x$ is $x = - \frac{1}{5} - \frac{3}{5} y$ . Substituting in other equation, we get

$[- \frac{1}{2} (- \frac{1}{5} - \frac{3}{5} y) - \frac{2}{3} y = \frac{5}{6}]$

$[\frac{3 - 11 y}{30} = \frac{5}{6}]$

Solve for y

On solving, we get

$[\frac{3 - 11 y}{30} = \frac{5}{6}]$

$y = - 2$

Substituting value to calculate $x$ , we get

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

Checking the value

Substituting, we get

$1 + \frac{3}{5} (- 2) = - \frac{1}{5} 1 - \frac{6}{5} = \frac{- 1}{5} - \frac{1}{5} = \frac{- 1}{5}$

Checking the value

Substituting, we get

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

So the value is correct

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Solve each system by elimination: $\{\begin{cases} x + \frac{3}{5} y = - \frac{1}{5} \\ - \frac{1}{2} x - \frac{2}{3} y = \frac{5}{6} \end{cases}$

Short Answer

Step by step solution

Given information

Isolate the value of x

Solve for y

Checking the value

Checking the value

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Solve each system by elimination:x+35y=-15-12x-23y=56

Short Answer

Step by step solution

Given information

Isolate the value of x

Solve for y

Checking the value

Checking the value

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Statistics

Applied Mathematics

Theoretical and Mathematical Physics

Geometry

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Solve each system by elimination: $\{\begin{cases} x + \frac{3}{5} y = - \frac{1}{5} \\ - \frac{1}{2} x - \frac{2}{3} y = \frac{5}{6} \end{cases}$