Question

In the following exercises, determine which ordered pairs are solutions to the given equations.

$y=6x-2$

1. $(1,4)$
   
2. $\left(\frac{1}{3},0\right)$
   
3. $\left(6,-2\right)$
   

Short answer

The solutions to the given equation are

1. $\left(1,4\right)$
2. $\left(\frac{1}{3},0\right)$
   

Step-by-step solution

. Given information

Equation is $y=6x-2$.......equation (1)

Points are

1. $(1,4)$
2. $\left(\frac{1}{3},0\right)$
   
3. $\left(6,-2\right)$
   

Part (a) Step 1. Check point (1,4) 

Substitute $x=1,y=4$in equation (1)

L.H.S.=$4$

R.H.S.=

$$\begin{gathered} 6\times 1-2 \\ =6-2 \\ =4 \end{gathered}$$

here L.H.S.=R.H.S.

So the point (1,4) is the solution to the equation.

Part(b) Step 1. To check point 13,0

Substitute $x=\frac{1}{3},y=0$in equation (1)

L.H.S.=0

R.H.S=

.$$\begin{gathered} 6\times \frac{1}{3}-2 \\ =2-2 \\ =0 \end{gathered}$$

here L.H.S.=R.H.S.

So the point $\left(\frac{1}{3},0\right)$is the solution to the equation.

Part(c) Step 1. To check point (6,-2) 

Substitute $x=6,y=-2$in equation (1)

L.H.S.=-2

R.H.S=
localid="1645008586176" $$\begin{gathered} 6\times 6-2 \\ =36-2 \\ =34 \end{gathered}$$

Since

$-2\ne 34$

Hence (6,-2) is not a solution to the equation.