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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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In Exercises 1-8, solve the system of equations.

{ x y = 8 2 x y = 2

To determine

To calculate: The solution of system of the equations x+y=8 and 2xy=2.

Explanation

Given Information:

The equations of the system are:

x+y=82xy=2

Formula used:

A system of linear equation can be solved using the method of elimination. To solve the system of equation using elimination follow the following procedure:

Step 1: Arrange both equations such that the like variables and constants are one above the other.

Step 2: Decide which variable to eliminate and with proper choice of multiplication, arrange so that the coefficients of that variable are same or opposite in sign for another.

Step 3: Add the equations if they are of opposite sign and subtract the equations if they are same sign leaving one equation with one variable.

Step 4: Solve for the remaining one variable.

Step 5: Substitute the value found in the above step in any equation involving both variables and solve for the other variable.

Calculation:

Consider the given equations

x+y=82xy=2

Solving the above equations by the method of elimination.

Eliminating the variable ‘yby adding the both equations as:

x+y+2xy=823x=6x=2

Substituting x=2 in x+y=8,

2+y=8y=82y=6

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