Question

How many solutions does this system of equations have?
y = 2x+5
y = 2x – 50

Answer 1

No solution

Explanation:

The system of equations y = 2x+5 and y = 2x – 50 has no solution.

This is because the two equations represent lines that are parallel.

Parallel lines never intersect, so they have no solution.

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Mathematically:

The system of equations y = 2x+5 and y = 2x – 50 can be solved by substitution method.

In substitution, we substitute the value of one variable in one equation into the other equation.

Let's substitute the equation y = 2x+5 into the equation y = 2x – 50.

`\sf 2x+5 = 2x – 50`

Subtracting both side by 2x, we get

`\sf 2x+5 -2x=2x-50-2x`

`\sf 5 = -50`

This is an inconsistent equation, which means that there are no solutions to the system of equations.