Chapter 11: Q. 1 (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.
$\{\begin{cases} 2 x - y = 5 \\ 5 x + 2 y = 8 \end{cases}$

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 equation $\{\begin{cases} 2 x - y = 5 \\ 5 x + 2 y = 8 \end{cases}$ .

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

Step 2. Eliminate the variable y and solve for x

Multiply both sides of the first equation $2 x - y = 5$ by $2$

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

Now add this equation with the first equation and solve for $x$ .

$\begin{array}{rcl} 5 x + 2 y + (4 x - 2 y) & = & 8 + 10 \\ 5 x + 2 y + 4 x - 2 y & = & 18 \\ 9 x & = & 18 \\ x & = & \frac{18}{9} \\ x & = & 2 \end{array}$

Step 3. Solve for y

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

$\begin{array}{rcl} 2 x - y & = & 5 \\ 2 \cdot 2 - y & = & 5 \\ 4 - y & = & 5 \\ - y & = & 5 - 4 \\ - y & = & 1 \\ y & = & - 1 \end{array}$

So the solution of the system is the ordered pair $(2, - 1)$ .

Step 4. Check the solution

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

$\begin{array}{rcl} 2 x - y & = & 5 \\ 2 \cdot 2 - (- 1) & = & 5 \\ 4 + 1 & = & 5 \\ 5 & = & 5 \\ 5 x + 2 y & = & 8 \\ 5 \cdot 2 + 2 (- 1) & = & 8 \\ 10 - 2 & = & 8 \\ 8 & = & 8 \end{array}$

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.
$\{\begin{cases} 2 x - y = 5 \\ 5 x + 2 y = 8 \end{cases}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Eliminate the variable 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.2x-y=55x+2y=8

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Eliminate the variable 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

Pure Maths

Calculus

Applied Mathematics

Logic and Functions

Probability and 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.
$\{\begin{cases} 2 x - y = 5 \\ 5 x + 2 y = 8 \end{cases}$