Which of these graphs shows that the linear system 3x+2y=12 and 6x+4y=24 has an infinite number of solutions?(1 point)
The graph that shows the two lines overlapping each other and having the same slope is the one that indicates the linear system has an infinite number of solutions. This is because if the two lines are overlapping, it means that they are representing the same line and therefore have an infinite number of solutions.
Solve the system of equations. 4x−8y=−36 −6x+y=32 (1 point)
To solve this system of equations, we can use the method of substitution or elimination.
First, let's solve the second equation for y:
-6x + y = 32
y = 6x + 32
Now, substitute this expression for y into the first equation:
4x - 8(6x + 32) = -36
4x - 48x - 256 = -36
-44x - 256 = -36
-44x = 220
x = 220 / (-44)
x = -5
Now, substitute x = -5 back into the second equation to solve for y:
-6(-5) + y = 32
30 + y = 32
y = 32 - 30
y = 2
Therefore, the solution to the system of equations 4x - 8y = -36 and -6x + y = 32 is x = -5, y = 2.
so the answer is 5, 2
No, the correct solution to the system of equations is x = -5, y = 2. So the answer is -5, 2.
Solve the system of equations. 6x−3y=−6 9x−3y=−18 (1 point)
To solve this system of equations, we can see that the equations are already in a form where the coefficients of y are the same. We can subtract the second equation from the first equation to eliminate y.
6x - 3y = -6
9x - 3y = -18
Subtracting the second equation from the first equation:
(6x - 3y) - (9x - 3y) = -6 - (-18)
6x - 3y - 9x + 3y = -6 + 18
-3x = 12
x = 12 / (-3)
x = -4
Now that we have found x, we can substitute x = -4 into one of the original equations to solve for y:
6(-4) - 3y = -6
-24 - 3y = -6
-3y = -6 + 24
-3y = 18
y = 18 / (-3)
y = -6
Therefore, the solution to the system of equations 6x - 3y = -6 and 9x - 3y = -18 is x = -4, y = -6.