Determine which system below will produce infinitely many solutions.
A.-6x+3y=18
4x-3y=6
B.2x+4y=24
6x+12y=36
C.3x-y=14
-9x+3y=-42
D.5x+2y=13
-x+4y=-6
Solve the system of equations.
x + 3y = −1
2x + 2y = 6
A.(-4,1)
B.(2,-1)
C.(4,-1)
D.(5,-2)
I think the answers are B for the first one and d for the second one.
To determine which system of equations will produce infinitely many solutions, we need to compare the slopes of the lines represented by the equations.
For system A:
Equation 1: -6x + 3y = 18 => y = 2x + 6
Equation 2: 4x - 3y = 6 => y = (4/3)x - 2
The slopes of both lines are different (2 and 4/3), so system A does not have infinitely many solutions.
For system B:
Equation 1: 2x + 4y = 24 => y = (-1/2)x + 6
Equation 2: 6x + 12y = 36 => y = (-1/2)x + 3
The slopes of both lines are the same (-1/2), so system B has infinitely many solutions.
For system C:
Equation 1: 3x - y = 14 => y = 3x - 14
Equation 2: -9x + 3y = -42 => y = 3x + 14
The slopes of both lines are the same (3), so system C has infinitely many solutions.
For system D:
Equation 1: 5x + 2y = 13 => y = (-5/2)x + (13/2)
Equation 2: -x + 4y = -6 => y = (1/4)x - (3/2)
The slopes of both lines are different (-5/2 and 1/4), so system D does not have infinitely many solutions.
Therefore, the systems that will produce infinitely many solutions are B and C.
Now, let's solve the second system of equations:
Equation 1: x + 3y = -1
Equation 2: 2x + 2y = 6
We can solve this system by using the method of substitution or elimination.
Method of substitution:
From Equation 1, solve for x:
x = -1 - 3y
Substitute the expression for x in Equation 2:
2(-1 - 3y) + 2y = 6
-2 - 6y + 2y = 6
-4y = 8
y = -2
Substitute the value of y back into Equation 1:
x + 3(-2) = -1
x - 6 = -1
x = 5
The solution for the system of equations is (x, y) = (5, -2).
Therefore, the correct answer is D. (5, -2).
yes.
1B no. 36 ≠ 24*3
2D ok