Chapter 11: Q. 5 (page 793)

In Problems 1–10, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, say that it is inconsistent.
$\{\begin{cases} x - 3 y + 4 = 0 \\ \frac{1}{2} x - \frac{3}{2} y + \frac{4}{3} = 0 \end{cases}$

Short Answer

Expert verified

The given system is inconsistent.

Step by step solution

Step 1. Given Information

We are given a system of equations $\{\begin{cases} x - 3 y + 4 = 0 \\ \frac{1}{2} x - \frac{3}{2} y + \frac{4}{3} = 0 \end{cases}$ .

We need to solve the system of using the method of substitution or the method of elimination.

Step 2. Use elimination method

Multiply the second equation by $2$ .

$\begin{array}{rcl} 2 (\frac{1}{2} x - \frac{3}{2} y + \frac{4}{3}) & = & 2 \cdot 0 \\ x - 3 y + \frac{8}{3} & = & 0 \end{array}$

Now subtract this equation from the first equation.

role="math" $\begin{array}{rcl} x - 3 y + 4 - (x - 3 y + \frac{8}{3}) & = & 0 - 0 \\ x - 3 y + 4 - x + 3 y - \frac{8}{3} & = & 0 \\ 4 - \frac{8}{3} & = & 0 \\ \frac{4}{3} & = & 0 \end{array}$

The statement formed is false.

So the given system has no solution and thus is inconsistent.

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In Problems 1–10, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, say that it is inconsistent.
$\{\begin{cases} x - 3 y + 4 = 0 \\ \frac{1}{2} x - \frac{3}{2} y + \frac{4}{3} = 0 \end{cases}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Use elimination method

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In Problems 1–10, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, say that it is inconsistent. x-3y+4=012x-32y+43=0

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Use elimination method

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Probability and Statistics

Pure Maths

Geometry

Calculus

Decision Maths

Study anywhere. Anytime. Across all devices.

In Problems 1–10, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, say that it is inconsistent.
$\{\begin{cases} x - 3 y + 4 = 0 \\ \frac{1}{2} x - \frac{3}{2} y + \frac{4}{3} = 0 \end{cases}$