Chapter 3: Q5. (page 119)

Solve each system of equations by using substitution
$\begin{matrix} 4 c + 2 d = 10 \\ c + 3 d = 10 \end{matrix}$

Short Answer

Expert verified

The solution of the system of equations is $(1, 3)$ .

Step by step solution

Step-1 – Apply the substitution method of solving equations

The algebraic method of substitution involves solving the one of the two equations for one variable in terms of other variable and then substituting the expression so formed for the variable in the second equation.

Step-2 – Solving one equation for c in terms of d

To solve the equation $c + 3 d = 10$ for cin terms of d, subtract 3d from both sides as shown below.

$\begin{matrix} c + 3 d = 10 \\ c + 3 d - 3 d = 10 - 3 d \\ c = 10 - 3 d \end{matrix}$

Step-3 – Substitute the expression

Now, substitute $c = 10 - 3 d$ in the first equation $4 c + 2 d = 10$ and solve for d.

$\begin{matrix} 4 c + 2 d = 10 \\ 4 (10 - 3 d) + 2 d = 10 \\ 40 - 12 d + 2 d = 10 \\ - 10 d = - 30 \end{matrix}$

Simplify it further as

$\begin{matrix} - 10 d = - 30 \\ d = 3 \end{matrix}$

Thus, the value of d is $3$ .

Step-4 – Substitute the value of variable

To find the value of c, substitute $d = 3$ in the equation $c + 3 d = 10$ and then solve for c as shown.

$\begin{matrix} c + 3 d = 10 \\ c + 3 (3) = 10 \\ c + 9 = 10 \\ c = 1 \end{matrix}$

Thus, the value of c is $1$ .

Hence, the solution of the provided system of equations is $(1, 3)$ .

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Solve each system of equations by using substitution
$\begin{matrix} 4 c + 2 d = 10 \\ c + 3 d = 10 \end{matrix}$

Short Answer

Step by step solution

Step-1 – Apply the substitution method of solving equations

Step-2 – Solving one equation for c in terms of d

Step-3 – Substitute the expression

Step-4 – Substitute the value of variable

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Solve each system of equations by using substitution 4c+2d=10 c+3d=10

Short Answer

Step by step solution

Step-1 – Apply the substitution method of solving equations

Step-2 – Solving one equation for c in terms of d

Step-3 – Substitute the expression

Step-4 – Substitute the value of variable

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Statistics

Geometry

Mechanics Maths

Probability and Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Solve each system of equations by using substitution
$\begin{matrix} 4 c + 2 d = 10 \\ c + 3 d = 10 \end{matrix}$