Question

What is the solution of the system of equations below?

2x + 3y = 7
x + y = 3
(1) (1,2)
(2) (2,1)
(3) (4,-1)
(4) (4,1)

Answer 1

2x + 3y = 7
x + y = 3

x = 3 - y

substituting for x,

2(3 - y) + 3y = 7

= 6 - 2y + 3y = 7
6 + y = 7

thus, y = 1

x = 3 - y

= 3 - 1
= 2.

Thus, x = 2 , y = 1

Thus, (2) is correct.

Answer 2

`\begin{cases}2x + 3y = 7 \\ x + y = 3 \ \ / *(-2) \end{cases}\\ \\\begin{cases}2x + 3y = 7 \\ -2x - 2y = -6\end{cases}\\+ \ ------- \\y=1\\ \\2x + 3\cdot1 = 7`


`2x+3=7 \ \ |-3\\ \\ 2x+3-3=7-3\\ \\2x=4 \ \ /:2 \\ \\x=2 \\ \\ \begin{cases} x=2 \\ y=1 \end{cases}`