Question

How many solutions does this system have `2x +8y= 16, -3x +6y =30`?

Answer 1

See a solution process below:

Explanation:

Even though the first equation is not in pure standard form we can write it as one. The standard form of a linear equation is: `color(red)(A)x + color(blue)(B)y = color(green)(C)`

Where, if at all possible, `color(red)(A)`, `color(blue)(B)`, and `color(green)(C)`are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

`color(red)(2)x + color(blue)(8)y = color(green)(16)`

The slope of an equation in standard form is: `m = -color(red)(A)/color(blue)(B)`

Substituting gives:

`m_1 = -color(red)(2)/color(blue)(8) = -1/4`

Even though the second equation is also not in pure standard form we can write it as one.

`color(red)(-3)x + color(blue)(6)y = color(green)(30)`

The slope for this equation is then:

`m_2 = -color(red)(-3)/color(blue)(6) = 1/2`

Because both slopes are different there is one solution to this system of equations.