Chapter 1.5, Problem 14E

Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Chapter
Section

Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

In Problems 11-22, solve each system by elimination or by any convenient method. { 5 x − 2 y = 4 2 x − 3 y = 5

To determine

To calculate: The solution of the system of equations {5x2y=42x3y=5 by using elimination method.

Explanation

Given Information:

The given equations are:

5xâˆ’2y=4 â€¦â€¦ (1)

2xâˆ’3y=5 â€¦â€¦ (2)

Formula used:

Elimination method:

To solve the system of equations, first transform the system and cancel out one variable. After that, solve the obtained equation for the variable involved. Now, substitute the value of the obtained variable into any of the original equations to get the value of another variable.

Calculation:

Multiply equation (1) with 2 and equation (2) with 5.

10xâˆ’4y=8 â€¦â€¦ (3)

10xâˆ’15y=25 â€¦â€¦ (4)

Subtract equation (3) from equation (4).

10xâˆ’15yâˆ’10x+4y=25âˆ’8âˆ’11y=17y=âˆ’1711

Substitute âˆ’1711 for y in the equation (1) and solve for x.

5xâˆ’2(âˆ’1711)=45x=4âˆ’34115x=1011x=211

Check the solution x=211

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