Question

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

Answer 1

Answer: 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 2

one solution: (2.5, 0)

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)