Question

Solve the following by substitution : -

x + y = 10
x - y = 5

Answer 1

Your question is -

x + y = 10
x - y = 5

Now, let us solve this system by the substitution method.

According to equation 2 ,

x - y = 5

thus, x = 5 + y

Substituting the value of x in equation 1,

(5 + y) + y = 10

5 + 2y = 10

2y = 10 - 5 = 5

thus, y = 5/2


Substituting the value of y in value of x,

x = 5 + y

= 5 + 5/2

= 15/2

Thus, x = 15/2 ( or 7.5) y = 5/2 ( or 2.5)

Answer 2

`\begin{cases} x + y = 10 \\ x - y = 5 \end{cases}\\ \\ \begin{cases} y = 10 -x\\ x - y = 5 \end{cases}\\ \\ \begin{cases} y = 10 -x\\ x - (10-x) = 5 \end{cases}\\ \\ \begin{cases} y = 10 -x\\ x - 10+x = 5 \end{cases}\\ \\`


`\begin{cases} y = 10 -x\\ 2x - 10 = 5 \end{cases}\\ \\\begin{cases} y = 10 -x\\ 2x = 5 +10 \end{cases}\\ \\ \begin{cases} y = 10 -x\\ 2x =15 \ \ /:2 \end{cases}\\ \\ \begin{cases} y = 10 -x\\ x =(15)/(2) \end{cases}\\ \\`


`\begin{cases} y = 10 - 7(1)/(2)\\ x =7(1)/(2) \end{cases}\\ \\ \begin{cases} y = 2(1)/(2)\\ x = 8(1)/(2) \end{cases}\\ \\`