Chapter 6: Q13. (page 393)

Use elimination to solve each system of equations.
$\begin{matrix} 2 x + 6 y = 18 \\ 3 x + 2 y = 13 \end{matrix}$

Short Answer

Expert verified

The solution of the given system of equations is $(3, 2)$ .

Step by step solution

Step 1. Write the given system of equations.

The given system of equations is:

$\begin{matrix} 2 x + 6 y = 18 . . . . . . (1) \\ 3 x + 2 y = 13 . . . . . . (2) \end{matrix}$

Step 2. Solve the given system of equations.

Multiply the both sides of the equation (2) by 3.

$\begin{array}{l} (3 x + 2 y) \times 3 = 13 \times 3 \\ 9 x + 6 y = 39 (3) \end{array}$

Subtract the equation (3) from equation (1) to eliminate the variable $y$ .

$\begin{array}{l} 2x + 6 y = 18 \\ 9 x + 6 y = 39 \\ \underline{- - -} \\ - 7 x = - 21 \\ x = \frac{- 21}{- 7} \\ x = 3 \end{array}$

The value of $x$ is 3.

Substitute 3 for $x$ in the equation (1) to find the value of $y$ .

$\begin{matrix} 2 x + 6 y = 18 \\ 2 (3) + 6 y = 18 \\ 6 + 6 y = 18 \\ 6 y = 18 - 6 \\ 6 y = 12 \\ y = \frac{12}{6} \\ y = 2 \end{matrix}$

The value of $y$ is 2.

Therefore, the solution of the given system of equations is $(3, 2)$ .

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Use elimination to solve each system of equations.
$\begin{matrix} 2 x + 6 y = 18 \\ 3 x + 2 y = 13 \end{matrix}$

Short Answer

Step by step solution

Step 1. Write the given system of equations.

Step 2. Solve the given system of equations.

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Use elimination to solve each system of equations.2x+6y=183x+2y=13

Short Answer

Step by step solution

Step 1. Write the given system of equations.

Step 2. Solve the given system of equations.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Calculus

Geometry

Mechanics Maths

Pure Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

Use elimination to solve each system of equations.
$\begin{matrix} 2 x + 6 y = 18 \\ 3 x + 2 y = 13 \end{matrix}$