Question

The pair of straight lines $x+y=2$ and $x=-2y+6$ have

• A. One solution
• B. Two solutions
• C. No solution
• D. Infinite solutions

Answer 1

The correct option is A One solution

Given lines :
$x+y=2$ and
$x=-2y+6$
Write the above lines in the slope intercept form $y=mx+b$.
So,
$x+y=2$
$\Rightarrow y=-x+2$
and
$x=-2y+6$
$\Rightarrow y=-\frac{1}{2}x+3$

Slopes of above lines are $-1$ and $-\frac{1}{2}$ which are different. Hence the given system has one solution.