Chapter 11: Q. 3 (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.
$\{\begin{cases} x - 2 y - 4 = 0 \\ 3 x + 2 y - 4 = 0 \end{cases}$

Short Answer

Expert verified

The solution of the system is $(2, - 1)$ .

Step by step solution

Step 1. Given Information

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

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

Step 2. Eliminate y and solve for x

Add the two equations and eliminate $y$ .

$\begin{array}{rcl} x - 2 y - 4 + 3 x + 2 y - 4 & = & 0 \\ 4 x - 8 & = & 0 \end{array}$

Now solve the equation for $x$

$\begin{array}{rcl} 4 x - 8 + 8 & = & 0 + 8 \\ 4 x & = & 8 \\ x & = & 2 \end{array}$

Step 3. Solve for y

Substitute $2$ for $x$ in the first equation and solve for $y$ .

$\begin{array}{rcl} x - 2 y - 4 & = & 0 \\ 2 - 2 y - 4 & = & 0 \\ - 2 y - 2 & = & 0 \\ - 2 y & = & 2 \\ y & = & - 1 \end{array}$

So the solution is given by the ordered pair $(2, - 1)$ .

Step 4. Check the solution

Substitute $2$ for $x$ and $- 1$ for $y$ in both the equations.

$\begin{array}{rcl} x - 2 y - 4 & = & 0 \\ 2 - 2 \cdot (- 1) - 4 & = & 0 \\ 2 + 2 - 4 & = & 0 \\ 4 - 4 & = & 0 \\ 0 & = & 0 \\ 3 x + 2 y - 4 & = & 0 \\ 3 \cdot 2 + 2 \cdot (- 1) - 4 & = & 0 \\ 6 - 2 - 4 & = & 0 \\ 6 - 6 & = & 0 \\ 0 & = & 0 \end{array}$

So both the equations are satisfied. Thus the found solution is correct.

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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.
$\{\begin{cases} x - 2 y - 4 = 0 \\ 3 x + 2 y - 4 = 0 \end{cases}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Eliminate y and solve for x

Step 3. Solve for y

Step 4. Check the solution

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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-2y-4=03x+2y-4=0

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Eliminate y and solve for x

Step 3. Solve for y

Step 4. Check the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Decision Maths

Mechanics Maths

Theoretical and Mathematical Physics

Geometry

Statistics

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.
$\{\begin{cases} x - 2 y - 4 = 0 \\ 3 x + 2 y - 4 = 0 \end{cases}$