Chapter 11: Q. 7 (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.
$\{\begin{cases} 2 x + 5 y = 10 \\ 4 x + 10 y = 20 \end{cases}$

Short Answer

Expert verified

The system has infinitely many solutions.

Step by step solution

Step 1. Given Information

We are given a system of equations $\{\begin{cases} 2 x + 5 y = 10 \\ 4 x + 10 y = 20 \end{cases}$ .

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

Step 2. Eliminate the variables

Multiply both sides of the first equation $2 x + 5 y = 10$ by $2$ .

role="math" $\begin{array}{rcl} 2 (2 x + 5 y) & = & 2 \cdot 10 \\ 4 x + 10 y & = & 20 \end{array}$

Now subtract this equation from the second equation.

$\begin{array}{rcl} 4 x + 10 y - (4 x + 10 y) & = & 20 - 20 \\ 4 x + 10 y - 4 x - 10 y & = & 0 \\ 0 & = & 0 \end{array}$

So we get a true statement.

So the system of equations have infinitely many solutions.

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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.
$\{\begin{cases} 2 x + 5 y = 10 \\ 4 x + 10 y = 20 \end{cases}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Eliminate the variables

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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. 2x+5y=104x+10y=20

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Eliminate the variables

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Geometry

Discrete Mathematics

Statistics

Decision Maths

Mechanics 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.
$\{\begin{cases} 2 x + 5 y = 10 \\ 4 x + 10 y = 20 \end{cases}$