Question

What is the solution to the system of equations? 2x – y = 7 y = 2x + 3 (2, 3) (2, 7) no solution infinite number of solutions

Answer 1

Option C.

Explanation:

Let
`a_1x+b_1y+c_1=0` and
`a_2x+b_2y+c_2=0` are two line.

If
`(a_1)/(a_2)=(b_1)/(b_2)=(c_1)/(c_2)`, then system of equations have infinite number of solutions.

If
`(a_1)/(a_2)=(b_1)/(b_2)\\eq (c_1)/(c_2)`, then system of equations have no solution.

If
`(a_1)/(a_2)\\eq (b_1)/(b_2)`, then system of equations have unique solution.

The given equations are

`2x-y=7`

`y=2x+3`

These equations can be rewritten as

`2x-y-7=0`

`2x-y+3=0`

Here,
`a_1=2,b_1=-1,c_1=-7,a_2=2,b_2=-1,c_2=3`.

`(a_1)/(a_2)=(2)/(2)=1`

`(b_1)/(b_2)=(-1)/(-1)=1`

`(c_1)/(c_2)=(-7)/(3)`

Since,
`(a_1)/(a_2)=(b_1)/(b_2)\\eq (c_1)/(c_2)`, therefore, the system of equations have no solution.

Hence, option C is correct.