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How many solutions does this linear system have?

a) one solution: (–2.5, 0)
b) one solution: (2.5, 0)
c) no solution
d) infinite number of solutions

User Pavel P
by
7.9k points

1 Answer

1 vote

Final answer:

In this case, the linear system has one solution: (2.5, 0)

The answer is option ⇒b.

Step-by-step explanation:

To find the solution to the given system of equations, we substitute the value of y from the first equation into the second equation.

The first equation is y = 2x - 5.

In the second equation, -8x - 4y = -20, we replace y with 2x - 5:

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

Simplifying this equation, we distribute the -4:

-8x - 8x + 20 = -20.

Combining like terms, we have:

-16x + 20 = -20.

To isolate the variable x, we subtract 20 from both sides of the equation:

-16x = -40.

Dividing both sides by -16, we get:

x = -40 / -16.

Simplifying, we have:

x = 2.5.

Now that we have found the value of x, we can substitute it back into the first equation to find the value of y.

Using the first equation y = 2x - 5, we replace x with 2.5:

y = 2(2.5) - 5.

Simplifying, we have:

y = 5 - 5.

Further simplifying, we find:

y = 0.

Therefore, the solution to the given system of equations is x = 2.5 and y = 0.

The answer is option ⇒b) one solution: (2.5, 0)

Your question is incomplete, but most probably the full question was:

How many solutions does this linear system have?

y = 2x – 5

–8x – 4y = –20

Options:

A- one solution: (–2.5, 0)

B- one solution: (2.5, 0)

C- no solution

D- infinite number of solutions

User Egerhard
by
8.2k points

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