# 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)

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.

answer: the anser is 3

step-by-step explanation:

c- 2o is equal to 9

tangent

step-by-step explanation: