Chapter 6: Q18. (page 389)

Use substitution to solve each system of equations.
$\begin{array}{l} x + y = 3 \\ x = 2 y \end{array}$

Short Answer

Expert verified

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

Step by step solution

Step 1. State the concept of substitution method to solve system of equations.

The substitution method is used to find the set of solutions for the given system of equations. It is the method in which one variable is first solved in the form of another variable.

So, the value of one variable in the form second variable is put on the second equation. It will give the solution of the one variable. And then solve it for another variable.

Step 2. Solve at least one equation for one variable and substitute.

The given system of equation is:

$x + y = 3$ … (1)

$x = 2 y$ … (2)

Note that in equation (2), variable x is in terms of y, therefore, put value of x in eq. (1):

localid="1647628963556" $x + y = 3 2 y + y = 3 Substitute x = 2 y 3 y = 3 Combineliketerms y = 1 Divideeachsideby3$

Step 3. Solve for x.

Substitute 1 for y into the equation (2) and solve for x.

$x = 2 y x = 2 (1) = 2$

The solution is $(2, 1)$ .

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Use substitution to solve each system of equations.
$\begin{array}{l} x + y = 3 \\ x = 2 y \end{array}$

Short Answer

Step by step solution

Step 1. State the concept of substitution method to solve system of equations.

Step 2. Solve at least one equation for one variable and substitute.

Step 3. Solve for x.

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Use substitution to solve each system of equations.x+y=3x=2y

Short Answer

Step by step solution

Step 1. State the concept of substitution method to solve system of equations.

Step 2. Solve at least one equation for one variable and substitute.

Step 3. Solve for x.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Calculus

Statistics

Pure Maths

Discrete Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Use substitution to solve each system of equations.
$\begin{array}{l} x + y = 3 \\ x = 2 y \end{array}$