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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 210 (page 444)

Solve Systems of Equations Using Matrices In the following exercises, solve each system of equations using a matrix.
$\{\begin{cases} 2 x + y = 2 \\ x - y = - 2 \end{cases}$

Short Answer

Expert verified

The solution of the system of equations is $(0, 2)$

Step by step solution

01

Step 1. Given Information

A system of equations is given as

$\{\begin{cases} 2 x + y = 2 \\ x - y = - 2 \end{cases}$

02

Step 2. Calculating Matrix

System of equations is given as

$\{\begin{cases} 2 x + y = 2 \\ x - y = - 2 \end{cases}$

First convert into argument matrix-

$[\begin{array}{r} 2 & 1 & 2 \\ 1 & - 1 & - 2 \end{array}]$

Then make zeroes in the matrix as-

$[\begin{array}{r} 2 & 1 & 2 \\ 1 & - 1 & - 2 \end{array}] \overset{R_{1} 鈫� R_{2}}{鉄�} [\begin{array}{r} 1 & - 1 & - 2 \\ 2 & 1 & 2 \end{array}] \overset{- 2 R_{1} + R_{2}}{鉄�} [\begin{array}{l} 1 & - 1 & - 2 \\ (- 2 脳 1) + 2 & (- 2 (- 1)) + 1 & (- 2 (- 2)) + 2 \end{array}] \overset{- 2 R_{1} + R_{2}}{鉄�} [\begin{array}{r} 1 & - 1 & - 2 \\ 0 & 3 & 6 \end{array}] \overset{\frac{1}{3} R_{2}}{鉄�} [\begin{array}{r} 1 & - 1 & - 2 \\ 0 & 1 & 2 \end{array}]$

03

Step 3. Verification

Verify the equation,

$x - y = - 2 0 - 2 = - 2 - 2 = - 2$

LHS is equal to RHS

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