Question

How do you solve the system of equations `y=-2x+5` and `y=-2x+20`?

Answer 1

No solution

Explanation:

The slope of the lines represented by the two equations is same, that is -2. The two lines are thus parallel and will never intersect. Hence there would be no solution.

Answer 2

See a solution process below:

Explanation:

Both of these equations are in slope-intercept form. The slope-intercept form of a linear equation is: `y = color(red)(m)x + color(blue)(b)`

Where `color(red)(m)` is the slope and `color(blue)(b)` is the y-intercept value.

`y = color(red)(-2)x + color(blue)(5)`

`y = color(green)(-2)x + color(purple)(20)`

The slope of the two equations are:

`color(red)(m_1 = -2)` and `color(green)(m_2 = -2)`

Because the have the same slope it means the lines represented by these two equations are either parallel or are the same line.

The `y`-intercepts for the two lines are:

`color(blue)(b_1 = 5)` and `color(purple)(b_1 = 20)`

Because these are not the same points these equations can't represent the same lines. Therefore these two equations represent parallel but different lines.

Therefore, the is no common point of solution to this problem.

Or, the solution is the empty or null set: `{O/}`

Answer 3

There is no solution.

The lines are parallel and will never intersect.

Explanation:

We can try to solve these as a system of equations.

We have

`color(blue)(y) =-2x +5" and "color(blue)(y) =-2x +20`

`color(white)(wwwwwwwwww)color(blue)(y) = color(blue)(y)`

`:. -2x+5 = -2x+20`

`" "-2x+2x = 20-5`

`color(white)(wwwwwww)0 = 15`

This is a false statement and there is no `x`.

This is an indication that there is no solution to the equations.

(As explained elsewhere, the lines have the same slope `(-2)` and are therefore parallel and will never intersect.)