Check whether (-4, -12) is a solution of the system of equations.
y = 6x + 12
2x - y = 4
When the graphs of two equations are parallel, there are infinitely many solutions.
y = x + 4
y = 3x
solution: ( , )
#1.
first equation:
LS = -12
RS = 6(-4) + 12 = -12
2nd equation:
LS = 2(-4) - (-12)
= -8 + 12 = 4
RS = 4
So, yes , it is a solution.
#2.
since y = x+4 and y = 3x , then
3x = x+4
2x = 4
x = 2
sub into either one of the two original equations ...
if x = 2, y = 6
so the solution is (2,6)
(Neither pair is parallel, I don't know why the statement about parallel lines was made.)
To check if (-4, -12) is a solution of the system of equations, we need to substitute the values of x and y into each equation and check if both equations are true.
For the first equation, y = 6x + 12, let's substitute x and y:
(-12) = 6(-4) + 12
-12 = -24 + 12
-12 = -12
The equation is true, so (-4, -12) is a solution to the first equation.
For the second equation, 2x - y = 4, let's substitute x and y:
2(-4) - (-12) = 4
-8 + 12 = 4
4 = 4
The equation is true, so (-4, -12) is a solution to the second equation.
Therefore, (-4, -12) is a solution to the system of equations.
Additional Note:
The last part of the question asks about a system of equations with missing information (solution: ( , )). It seems like the question is incomplete, as there are no specific equations given for that system. Please provide the equations, so I can assist you further.