Chapter 9.6, Problem 60SR

To determine

The solution of each equations

  $\begin{array}{l}x+y=-3\mathrm{......}\left(\text{i}\right)\\ x-y=1\mathrm{......}\left(\text{ii}\right)\end{array}$

Answer to Problem 60SR

The solution of the equation is $x=-1\text{and}y=-2$ .

Explanation of Solution

Given:

The equations are $\begin{array}{l}x+y=-3\mathrm{......}\left(\text{i}\right)\\ x-y=1\mathrm{......}\left(\text{ii}\right)\end{array}$

Concept Used:

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to solve the given equation

  $\begin{array}{l}x+y+3=0\mathrm{......}\left(\text{i}\right)\\ x-y-1=0\mathrm{......}\left(\text{ii}\right)\\ \end{array}$

for the variable, isolate the variable term x and y on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate x on both equation, first we need to subtract equation (i) from equation (ii) as shown below,

  $\begin{array}{l}x+y+3=0\mathrm{......}\left(i\right)\\ x-y-1=0\mathrm{......}\left(ii\right)\\ \left(x+y+3\right)-\left(x-y-1\right)=0\\ x+y+3-x+y+1=0\\ 2y+4=0\\ 2y+4-4=-4\\ 2y=-4\\ \frac{2y}{2}=\frac{-4}{2}\\ y=-2\\ \text{put the value of y in equation}\left(i\right)\\ x+y+3=0\\ x-2+3=0\\ x+1=0\\ x+1-1=-1\\ x=-1\end{array}$

Thus, the solution of the equation is $x=-1\text{and}y=-2$ .