Question

Without solving the systems, explain why the following systems must have the same solution.

System (i): 4x−5y=13
3x+6y=11
System (ii): 8x−10y=26
x−11y=2

Answer 1

Both system of equations are intersecting

Explanation:

The equations are of the form

ax+by+c=0

Two equations have no solution when

`(a_1)/(a_2)=(b_1)/(b_2)=(c_1)/(c_2)`

i) 4x−5y-13=0

3x+6y-11=0

`(4)/(3)\\eq (5)/(6)\\eq (13)/(11)`

So, they are intersecting lines and do have the same solution.

ii) 8x−10y-26=0

x−11y-2=0

`(8)/(1)\\eq (-10)/(-11)\\eq (13)/(11)`

So, they are intersecting lines and do have the same solution.