Question

determine the number of solutions for the system of linear equations

y = -10x + 5
300 = -15x + 60y

Answer 1

solve = -8x + 32 = -16

Answer 2

To find the number of solutions for the system of linear equations, we need to determine if they intersect at a single point, are parallel lines, or are coincident lines.

First, let's rewrite the equations in standard form:

10x + y = 5 (equation 1)
15x - 60y = -300 (equation 2)

To find the number of solutions, we can compare the slopes of the lines represented by the equations.

The slope of equation 1 is -10, and the slope of equation 2 is 1/4 (15/60).

Since the slopes are different, the lines represented by the equations are not parallel.

Now, let's solve the system of equations to see if they intersect at a single point:

10x + y = 5 (equation 1)
15x - 60y = -300 (equation 2)

Rearranging equation 1, we have:
y = -10x + 5

Substituting this into equation 2, we get:
15x - 60(-10x + 5) = -300
15x + 600x - 3000 = -300
615x - 3000 = -300
615x = 2700
x = 2700/615
x = 4.39 (approx)

Substituting x = 4.39 back into equation 1:
y = -10(4.39) + 5
y = -43.9 + 5
y = -38.9

Therefore, the system of linear equations intersects at a single point (4.39, -38.9).

The number of solutions for the system of linear equations is 1.

Answer 3

To solve the equation -8x + 32 = -16, we can follow these steps:

1. Start with the given equation: -8x + 32 = -16

2. Subtract 32 from both sides to isolate the term with x:
-8x + 32 - 32 = -16 - 32
-8x = -48

3. Divide both sides by -8 to solve for x:
-8x / -8 = -48 / -8
x = 6

Therefore, the solution to the equation -8x + 32 = -16 is x = 6.