Asked by Kaitlyn
Solve each system using substitution. Tell whether the system has one solution, infinitely solutions, or no solution.
1.)
2x + y = -12;-4x - 2y = 30
2.)
1/3y = 7/3x + 5/3;x - 3y = 5
3.)
Y = X - 7;3x - 3y = 21
1.)
2x + y = -12;-4x - 2y = 30
2.)
1/3y = 7/3x + 5/3;x - 3y = 5
3.)
Y = X - 7;3x - 3y = 21
Answers
Answered by
Reiny
1.
2x + y = -12
-4x - 2y = 30 ---> 2x + y = -15
Clearly two parallel lines. I see the same slope, but different y-intercepts,
So obviously they cannot intersect
2.
1/3y = 7/3x + 5/3 ---> y = 7x + 5
x - 3y = 5
I see different slopes, so they WILL intersect
sub y = 7x + 5 into the 2nd
carry on
3.
Y = X - 7
3x - 3y = 21 ----> x - y = 7 or y = x - 7
They are both the same equation,
any equation will intersect with its self in an infinite number of points.
2x + y = -12
-4x - 2y = 30 ---> 2x + y = -15
Clearly two parallel lines. I see the same slope, but different y-intercepts,
So obviously they cannot intersect
2.
1/3y = 7/3x + 5/3 ---> y = 7x + 5
x - 3y = 5
I see different slopes, so they WILL intersect
sub y = 7x + 5 into the 2nd
carry on
3.
Y = X - 7
3x - 3y = 21 ----> x - y = 7 or y = x - 7
They are both the same equation,
any equation will intersect with its self in an infinite number of points.