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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 4: Q 60 (page 387)

In the following exercise, solve the systems of equations by elimination.
$\{\begin{cases} 2 x + y = 3 \\ 6 x + 3 y = 9 \end{cases}$

Short Answer

Expert verified

The given system has infinitely many solutions.

Step by step solution

01

Step 1. Given information

The given linear equations are :

$2 x + y = 3 6 x + 3 y = 9$

02

Step 2. Calculating the value of y

To calculate the value of $y$ , we have to eliminate the $x$ term. For which we will do the following changes in the equation, so that $x$ term can be easily eliminated.

Multiply the first equation by $- 3$

$- 3 (2 x + y = 3) - 6 x - 3 y = - 9$

now, the equations are

localid="1644466930167" $- 6 x - 3 y = - 9 6 x + 3 y = 9$

now simply add the equations

$- 6 x - 3 y = - 9 + 6 x + 3 y = 9 0 = 0$

this means that the above equation is satisfied for all the values of $x$ and $y$ .

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