Exercise 4 Page 159

To determine if the given equation is a linear equation, let's first see if we can rewrite it in standard form. Ax+ By= CIn this form, A, B, and C are constants and either A or B must be nonzero.

2/3x - 1/3 y = 2

MoveRightFacToNum

a/c* b = a* b/c

2x/3-y/3=2

MultEqn

LHS * 3=RHS* 3

(2x/3 - y/3) 3 = 2*3

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Simplify

Distr

Distribute 3

2x/3* 3 - y/3* 3 = 6

FracMultDenomToNumber

a/3* 3 = a

2x - y = 6

This is the standard form of the given equation. Below we have highlighted how it corresponds to the general standard form. 2x-y=6 ⇔ 2x+( -1)y= 6 When written this way, we can see that A= 2, B= -1, and C= 6. Since this equation can be written in standard form, it is linear.