Chapter 11: Q. 29 (page 740)

In Problems 15 – 42, solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so.
$\{\begin{cases} 2 x + 3 y = 6 \\ x - y = \frac{1}{2} \end{cases}$

Short Answer

Expert verified

The solution is $x = \frac{3}{2}, y = 1 and in ordered pair is (\frac{3}{2}, 1) .$

Step by step solution

Step 1. Given Information

The given system of equation is

$\{\begin{cases} 2 x + 3 y = 6 \\ x - y = \frac{1}{2} \end{cases}$

We have to solve the system of equations using Cramer's rule if it is applicable.

Step 2. Finding the determinant

The determinant D of the coefficients of the variables is

$D = |\begin{matrix} 2 & 3 \\ 1 & - 1 \end{matrix}| D = (2) (- 1) - (3) (1) D = (- 2) - (3) D = - 5$

Since $D \neq 0$ Cramer's rule is applicable.

Step 3. Use Cramer's rule

Let's find $D_{x} and D_{y}$

$D_{x} = |\begin{matrix} 6 & 3 \\ \frac{1}{2} & - 1 \end{matrix}| D_{x} = (- 1) (6) - (3) (\frac{1}{2}) D_{x} = - 6 - \frac{3}{2} D_{x} = - \frac{15}{2}$

And

$D_{y} = |\begin{matrix} 2 & 6 \\ 1 & \frac{1}{2} \end{matrix}| D_{y} = (2) (\frac{1}{2}) - (1) (6) D_{y} = 1 - 6 D_{y} = - 5$

Step 4. Finding x and y

By using Cramer's rule, the values of xand yare

$x = \frac{D_{x}}{D} a n d y = \frac{D_{y}}{D} x = \frac{- \frac{15}{2}}{- 5} a n d y = \frac{- 5}{- 5} x = \frac{3}{2} a n d y = 1$

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In Problems 15 – 42, solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so.
$\{\begin{cases} 2 x + 3 y = 6 \\ x - y = \frac{1}{2} \end{cases}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the determinant

Step 3. Use Cramer's rule

Step 4. Finding x and y

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In Problems 15 – 42, solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so.2x+3y=6x-y=12

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the determinant

Step 3. Use Cramer's rule

Step 4. Finding x and y

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Decision Maths

Mechanics Maths

Probability and Statistics

Pure Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In Problems 15 – 42, solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so.
$\{\begin{cases} 2 x + 3 y = 6 \\ x - y = \frac{1}{2} \end{cases}$