Chapter 3: Q6. (page 149)

6: Solve each system of equation by graphing, substitution, or elimination.
$\begin{matrix} 3 x + 2 y = 18 \\ y = 6 x - 6 \end{matrix}$

Short Answer

Expert verified

The solution is $x = 2, y = 6$ .

Step by step solution

Step-1 – Concept of elimination

The process of adding or subtracting equation to remove a variable and simplify solving the system of equations is called elimination.

Step-2 – Using elimination to solve the equation

Given equations are-:

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

Multiplying the first equation by $2$ and adding with second equation, we get

$\begin{matrix} 4 y + y = 36 - 6 \\ 5 y = 30 \\ y = 6 \end{matrix}$

Step-3–Substituting the value of y in first equation, we get

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

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6: Solve each system of equation by graphing, substitution, or elimination.
$\begin{matrix} 3 x + 2 y = 18 \\ y = 6 x - 6 \end{matrix}$

Short Answer

Step by step solution

Step-1 – Concept of elimination

Step-2 – Using elimination to solve the equation

Step-3–Substituting the value of y in first equation, we get

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6: Solve each system of equation by graphing, substitution, or elimination.3x+2y=18y=6x-6

Short Answer

Step by step solution

Step-1 – Concept of elimination

Step-2 – Using elimination to solve the equation

Step-3–Substituting the value of y in first equation, we get

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Logic and Functions

Applied Mathematics

Decision Maths

Discrete Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

6: Solve each system of equation by graphing, substitution, or elimination.
$\begin{matrix} 3 x + 2 y = 18 \\ y = 6 x - 6 \end{matrix}$