Chapter 9.1, Problem 2CE

To determine

Calculate the value of y at the given value of x and sketch a graph.

Answer to Problem 2CE

The solution is,

  

Explanation of Solution

Given: The algebraic equations are given,

  $\begin{array}{l}x+3y=1\\ \frac{1}{2}x-4y=-5\end{array}$

Calculation:

Let’s take the first equation,

  $x+3y=1$

Put the value of x, $x=-3$

Then simplify the equation and calculate the value of y.

  $\begin{array}{l}-3+3y=1\\ 3y=4\\ y=\frac{4}{3}\end{array}$

If we consider second equation $\frac{1}{2}x-4y=-5$ then,

  $\begin{array}{l}-\frac{3}{2}-4y=-5\\ 4y=5-\frac{3}{2}\\ 4y=\frac{7}{2}\\ y=\frac{7}{8}\end{array}$

program:

clc
clear
close all
symsxy
a=x+3*y-1;
b=x-4*y+5;
xx=-3:1:1;
fori=1:5
    s=subs(a,x,xx(i));
    sol(i)=solve(s);
    s1=subs(b,x,xx(i));
    sol1(i)=solve(s1);
end
plot(xx,sol,'linewidth',1.2)
hold on
plot(xx,sol1,'linewidth',1.2)
set(gca,'linewidth',1.2,'fontsize',12)
xlabel('x')
ylabel('y')
axis square

Query:

• First, we have defined both the algebraic equations.
• Then define the value of x.
• Then put the value of x into both the equations and calculate the value of y.
• Sketch a graph for y at different value of x.