Exercise 89 Page 504

The given system consists of the equations of two lines. Since the y-variable is already isolated in the first equation, we can use the Substitution Method to solve the system. y= 12x-4 & (I) x-4y=12 & (II)When a variable is isolated in one of the equations, we can substitute its equivalent expression into the remaining equation. Simplifying the resulting equation should isolate another variable. If we substitute Equation (I) into Equation (II), we will eliminate the y-variable and should be able to isolate the x-variable. Let's do it!

y= 12x-4 x-4y=12

Substitute

(II): y= 1/2x-4

y= 12x-4 x-4( 12x-4)=12

▼

(II): Solve for x

Distr

(II): Distribute -4

y= 12x-4 x-2x+16=12

SubTerm

(II): Subtract term

y= 12x-4 - x+16=12

SubEqn

(II): LHS-16=RHS-16

y= 12x-4 - x=-4

MultEqn

(II): LHS * (-1)=RHS* (-1)

y= 12x-4 x=4

The x-variable has now been isolated in the second equation. Let's substitute its equivalent expression into the first equation and solve for y!

y= 12x-4 x=4

Substitute

(I): x= 4

y= 12( 4)-4 x=4

▼

(I): Solve for y

Multiply

(I): Multiply

y=2-4 x=4

SubTerm

(I): Subtract term

y=-2 x=4

We found that x=4 and y=- 2. Since all answers are written in the form (x,y), let's write our answer as an ordered pair, too. The solution to the system is (4,-2), which matches option D.