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

Answer 1

See a solution process below:

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.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.