How many solutions does this linear system have? y = 2x – 5 –8x – 4y = –20 one solution: (–2.5, 0) one solution: (2.5, 0) no solution infinite number of solutions

one solution: (2.5, 0)

Step-by-step explanation:

y = 2x – 5  

–8x – 4y = –20

Solve the second equation for y

Add 8x to each side

–8x+8x – 4y =8x –20

-4y = 8x-20

Divide by -4

-4y/-4 =8x/-4 -20/-4

y = -2x+5

The two equations are

y = 2x-5

y = -2x+5

Both equations are solved for y so set them equal

2x-5 = -2x+5

Add 2x to each side

2x+2x-5 = -2x+2x+5

4x-5 = 5

Add 5 to each side

4x-5+5 = 5+5

4x=10

Divide by 4

4x/4 = 10/4

x = 2.5

y = 2x-5

Substitute x=2.5 in

y = 2(2.5) - 5

y=5-5

y=0

There is one solution (2.5,0)

Equation (1):
y = 2x - 5

Equation (2):
-8x - 4y = -20
(-8x - 4y = -20) /4   ⇒  Simplify by dividing each term by GCF 4 
-2x - y = -5

Substitution to find x:

-2x - y = -5
-2x - (2x - 5) = -5
-2x - 2x + 5 = - 5
-4x/-4 = (-5 -5)/-4
x = -10/-4
x = 5/2  or  2.5

Find y:
y = 2x - 5
y = 2(2.5) - 5
y = 5 - 5
y = 0

ANSWER: One solution (x,y) = (2.5, 0) 

Interpretation: The lines are intersecting and the system is consistent and independent.

Check:
y = 2x - 5
0 = 2(2.5) - 5
0 = 5-5
0 = 0  (True)

-2x - y = -5
-2(2.5) - 0 = -5
-5 = -5   (True)

@PrimAndProper

B (2.5, 0)

B: - One solution: (2.5, 0)                  

Step-by-step explanation:

Given : Two linear equation -

Equation 1 -  

Equation 2 -  

To find : How many solutions does this linear system have?

Solution :

We solve the given equations,

Substitute the value of y from equation 1 in equation 2

Now, put value of x in equation 1

There is one solution (x,y) = (2.5, 0)

B is correct.

Claude debussy's music was associated with answer choice 3, impressionist

step-by-step explanation:

the answer is 128