Chapter 3.1, Problem 64PPS

To determine

To solve the given system of linear equations.

Answer to Problem 64PPS

  $t=2.5,v=-3.$

Explanation of Solution

Given information: We have given a system of linear equations

  $\begin{array}{l}10t+4v=13\mathrm{...}\text{(1)}\\ -4t-7v=11\mathrm{...}\text{(2)}\end{array}$

Calculation: Let us solve the given system using Elimination method.

According to elimination method we need to eliminate a variable by adding or subtracting given equations in the system.

We need to make the coefficient same of a variable in both equations $10t+4v=13$ and $-4t-7v=11$ .

Let us try to eliminate variable v .

Coefficient of v in first and second equation are 4 and -7. Least common multiple of 4 and 7 is 28. So, let us make both coefficients as 28 with opposite signs.

Therefore, multiply equation $10t+4v=13$ by 7 and equation $-4t-7v=11$ by 4, we get

  $\begin{array}{l}\left(10t+4v=13\right)\times 7\Rightarrow 70t+28v=91\\ \left(-4t-7v=11\right)\times 4\Rightarrow -16t-28v=44\end{array}$

Now, adding above equations and simplify

  $\begin{array}{l}70t+28v=91\\ \underset{\_}{-16t-28v=44}\\ 54t=135\end{array}$

Divide both sides by 54, we get

  $\begin{array}{l}\frac{54t}{54}=\frac{135}{54}\\ \Rightarrow t=2.5\end{array}$

Plug $t=2.5$ in second equation $10t+4v=13$ .

  $\begin{array}{l}10(2.5)+4v=13\\ \Rightarrow 25+4v=13\end{array}$

Subtract 25 on both sides

  $\begin{array}{l}25+4v-25=13-25\\ \Rightarrow 4v=-12\end{array}$

Divide by 2 on both sides

  $\begin{array}{l}\frac{4v}{4}=\frac{-12}{4}\\ \Rightarrow v=-3\end{array}$

Therefore, the solutions of system is $t=2.5,v=-3.$