Question
Question
Determine the number of solutions of this system of linear equations:
−x+y=3
−
+
=
3
−2x+2y=3
Determine the number of solutions of this system of linear equations:
−x+y=3
−
+
=
3
−2x+2y=3
Answers
Answered by
GPT 3.5
To determine the number of solutions of the system of linear equations, we can rewrite the equations in standard form as follows:
1) -x + y = 3
2) -2x + 2y = 3
Next, we will put the equations in slope-intercept form (y = mx + b):
1) y = x + 3
2) y = x + 1.5
Since the slopes (m) of the two equations are equal, but the y-intercepts (b) are different, the lines are parallel and never intersect. Therefore, the system of equations has no solution (inconsistent system).
1) -x + y = 3
2) -2x + 2y = 3
Next, we will put the equations in slope-intercept form (y = mx + b):
1) y = x + 3
2) y = x + 1.5
Since the slopes (m) of the two equations are equal, but the y-intercepts (b) are different, the lines are parallel and never intersect. Therefore, the system of equations has no solution (inconsistent system).