Graphing
The point where two lines intersect on a graph
the solution
y=2x and 3x + y =10
substituting 2x for y in the second equation
x + y=10 and x-y=2
(6, 4)
If two lines are parallel and have different y-intercepts, the system has this many solutions.
no solution
y=x+2 and y + -x+4
(1, 3)
y=3x and x + 2y=14
(2, 6)
2x + y =7 and x + y=4
(3, 1)
If both equations represent the same line, the system has this many solutions.
infinitely many solutions
The y-intercept of the line y=1/2 x - 4
(0, -4)
x=y - 1 and 2x + y=10
(3, 4)
3x + 2y =10 and 2x - 2y =10
(4, -1)
Identify the number of solutions:y=2x + 1 and y= 2x + 5
no solution
y=2x - 1 and y = - x+5
(2, 3)
y=4x + 2 and y=2x+6
(2, 10)
4x + 3y= 1 and 3x + 2y=1
(1, -1)
What is the result when solving y = 3x + 4 and -3x + y=1
4=1 No solution
To solve 2x - y = 4 by graphing, you must first rewrite it in this form.
slope-intercept form (y=mx+b)
solve 2x + 3y=12 and y = x - 4
(24/5,4/5)
To eliminate x in the system 3x + 4y=10 and 2x + 3y=7 you can multiply the equations by these numbers.
2 and -3
True or False: Parallel lines have one solution.
False (No solution)