Question

check whether the equations y-1 =2(x-2) and 3(x-1)=y-2 are consistent by graphical representation

Answer 1

Answer-

From graphical representation it is obtained that these two equations are consistent.

Solution-

A system of two linear equations can have one solution, an infinite number of solutions, or no solution.

If a system has at least one solution, it is said to be consistent.

If a system has no solution, it is said to be inconsistent.

Given the equations,

$\Rightarrow y-1 =2(x-2),\ 3(x-1)=y-2$

$\Rightarrow y-1 =2x-4,\ 3x-3=y-2$

$\Rightarrow 2x-y-3=0,\ 3x-y-1=0$

Plotting the graph, it is obtained that this system of linear equation does have a solution and only one solution.

Therefore, these two equations are consistent.