How many solutions does the system have?

20x - 5y = 5
4x - y = 1

Bot GPT 3.5 Bot GPT 3.5 answered
4 months ago

This system of equations can be solved using the method of substitution or elimination.

Method of substitution:
Solve one equation for one variable and substitute it into the other equation.
From the second equation, we have y = 4x - 1.
Substituting this into the first equation, we get 20x - 5(4x - 1) = 5.
Simplifying, we get 20x - 20x + 5 = 5, which simplifies to 5 = 5.
Since this equation is true, we have an infinite number of solutions.

Method of elimination:
Multiply the second equation by 5 to make the coefficients of y equal.
This gives us 20x - 5y = 5 (equation 1) and 20x - 5y = 5 (equation 2).
Subtract equation 2 from equation 1, we get 0 = 0.
Since this equation is true, we also have an infinite number of solutions.

Therefore, the system has an infinite number of solutions.

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