How many points of intersection does this system have? y = 3 x minus 4. Negative 3 x + y = 4.

You can start with y = 3x-4 and subtract 3x from both sides to get

y = 3x-4

y-3x = 3x-4-3x

-3x+y = -4

So the first equation transforms into -3x+y = -4

-----------------

We have this system of equations

The left hand side is the same expression. Let's make z = -3x+y

So our updated system is now

but this is not possible to have a single variable equal to more than one number at a time. Either z is -4 or it is 4, but it cannot be both at the same time.

Therefore, this system is considered inconsistent and it has no solutions.

If you were to graph each equation (as shown below), you would have two parallel lines that never cross. An intersection point is a solution to a system. Having no intersection points means there are no solutions.

b. 24 mm

step-by-step explanation:

use the pythagorean theorem.

a^2 + b^2 = c^2

a^2 + 7^2 = 25^2

a^2 + 49 = 625

a^2 = 576

a = 24

answer: b. 24 mm

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions