Chapter 4: Q. 69 (page 387)

Solve the system of equations by substitution and explain all your steps in words:
$\{\begin{cases} 3 x + y = 12 \\ x = y - 8 \end{cases}$

Short Answer

Expert verified

The solution of system of linear equation $\{\begin{cases} 3 x + y = 12 \\ x = y - 8 \end{cases}$ is $(1, 9)$

Step by step solution

Step 1. Given information and Solving equation

Given system of linear equations:

$\{\begin{cases} 3 x + y = 12 \\ x = y - 8 \end{cases}$

Firstly we will solve one equation for one valuable.

Consider equation $2$

Substitute $x = y - 8$ in equation

$3 x + y = 12$ and solve for $y .$

Consider:localid="1644340563247" $\begin{array}{r} 3 x + y = 12 \end{array}$

Substitute and simplify parenthesis:

$\begin{array}{r} 3 (y - 8) + y = 12 \\ 3 y - 24 + y = 12 \end{array}$

$4 y = 36$

$y = 36 \div 4$

$y = 9$

Step 2. Solving for x

Now let us substitute $y = 9$ into

$x = y - 8$ and solve for $x$

On substituting we get:

$x = 9 - 8 x = 1$

So the solution is: $(1, 9)$

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Solve the system of equations by substitution and explain all your steps in words:
$\{\begin{cases} 3 x + y = 12 \\ x = y - 8 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information and Solving equation

Step 2. Solving for x

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Solve the system of equations by substitution and explain all your steps in words:3x+y=12x=y-8

Short Answer

Step by step solution

Step 1. Given information and Solving equation

Step 2. Solving for x

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Mechanics Maths

Decision Maths

Logic and Functions

Probability and Statistics

Geometry

Study anywhere. Anytime. Across all devices.

Solve the system of equations by substitution and explain all your steps in words:
$\{\begin{cases} 3 x + y = 12 \\ x = y - 8 \end{cases}$