Answered

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

Verified Answer :

hannah152

The solution is (2.5,0)....

Answer:

Option 2 - One solution: (2.5, 0)                  

Step-by-step explanation:

Given : Two linear equation -

Equation 1 - \(y = 2x - 5\)

Equation 2 - \(-8x - 4y = -20\)

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

\(-8x - 4y = -20\)

\(-8x - 4(2x-5) = -20\)

\(-8x - 8x+20 = -20\)

\(-16x=-40\)

\(x=\frac{40}{16}\)

\(x=2.5\)

Now, put value of x in equation 1

\(y = 2x - 5\)

\(y = 2(2.5) - 5\)

\(y = 5 - 5\)

\(y = 0\)

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

Option 2 is correct.

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