Chapter 11: Q. 22 (page 796)

In Problems $21$ and $22$ , solve each system of equations.
$\{\begin{array}{r} 2 y^{2} - 3 x^{2} = 5 \\ y - x = 1 \end{array}$

Short Answer

Expert verified

Solution of system equations is $(1, 2) & (3, 4)$

Step by step solution

Step 1. Given information

A system of equations is given as

$\{\begin{array}{r} 2 y^{2} - 3 x^{2} = 5 \\ y - x = 1 \end{array}$

Step 2. Solving for x

First we will find the value of yin terms of x as,

$y - x = 1 y = 1 + x$

$2 y^{2} - 3 x^{2} = 5 2 (1 + x)^{2} - 3 x^{2} = 5 2 (x^{2} + 2 x + 1) - 3 x^{2} = 5 - x^{2} + 4 x + 2 - 5 = 0 x^{2} - 4 x + 3 = 0 (x - 3) (x - 1) = 0 x = 1, 3$

Now substitute the values of x as,

$y = 1 + 1 y = 2 & y = 1 + 3 y = 4$

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In Problems $21$ and $22$ , solve each system of equations.
$\{\begin{array}{r} 2 y^{2} - 3 x^{2} = 5 \\ y - x = 1 \end{array}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solving for x

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In Problems 21and 22, solve each system of equations. 2y2-3x2=5y-x=1

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solving for x

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Statistics

Logic and Functions

Decision Maths

Applied Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In Problems $21$ and $22$ , solve each system of equations.
$\{\begin{array}{r} 2 y^{2} - 3 x^{2} = 5 \\ y - x = 1 \end{array}$