Chapter 3.1, Problem 75PPS

(a)

To determine

To Make: A table for x and y values for the given equations.

Answer to Problem 75PPS

  $5\sec .$

Explanation of Solution

Given:given equations are.

  $\begin{array}{l}3y+x=16\\ y-2x=-4\\ y+5x=10\end{array}$

Calculation:

For the equation $3y+x=16$ , x and y values are given in the table below.

  $\begin{array}{cc}x& y\\ 0& \frac{16}{3}\\ 16& 0\end{array}$

For the equation $y-2x=-4$ , x and y values are given in the table below.

  $\begin{array}{cc}x& y\\ 0& -4\\ 2& 0\end{array}$

For the equation $y+5x=10$ , x and y values are given in the table below.

  $\begin{array}{cc}x& y\\ 0& 10\\ 2& 0\end{array}$

(b)

To determine

To Find;The value which indicates intersection and find the value which satisfy all three equation if any.

Answer to Problem 75PPS

  $\left(2,0\right)$ , No solution satisfies all three equations.

Explanation of Solution

Given; Table are given belowfor equations $3y+x=16$ , $y-2x=-4$ and $y+5x=10$

  $\begin{array}{cc}x& y\\ 0& \frac{16}{3}\\ 16& 0\end{array}$ , $\begin{array}{cc}x& y\\ 0& -4\\ 2& 0\end{array}$ and $\begin{array}{cc}x& y\\ 0& 10\\ 2& 0\end{array}$

Explanation; Only $\left(2,0\right)$ is the point of intersection of equations $y-2x=-4$ and $y+5x=10$ .

There is no solution which satisfies all three equations.

(c)

To determine

To Graph:Theequation in single coordinate plane.

Answer to Problem 75PPS

  $\left(2,0\right)$ , No solution satisfies all three equations.

Explanation of Solution

Given;

Table of x and y values for equations given below.

  $\begin{array}{cc}x& y\\ 0& \frac{16}{3}\\ 16& 0\end{array}$ , $\begin{array}{cc}x& y\\ 0& -4\\ 2& 0\end{array}$ and $\begin{array}{cc}x& y\\ 0& 10\\ 2& 0\end{array}$

Explanation;

Plotting graph with the help of table.

  

(d)

To determine

To Explain:The condition for a system of three equations with two variables to have a solution and to have no solution.

Explanation of Solution

Given;

A system of three equations with two variables.

Explanation;

For a system of three equations with two variables to have solution it must intersect at a point and to have no solution it must not intersect.