Question

What is the number of solutions for the given system of linear equations $y=2x+3$ and $x+y=1$?

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

Answer 1

The correct option is A One


Given lines :
$y=2x+3\dots$ $\left(1\right)$
$x+y=1\dots$ $\left(2\right)$
Step 1: Write those lines in slope-intercept form
So,
$\Rightarrow y=2x+3$
m = 2, b = 3
and
$x+y=1$
$\Rightarrow y=-x+1$
m = -1, b = 1

The slopes of two given equations are not the same. Thus, the given system intersects at a single point and has one solution.