Exercise 88 Page 344

Practice makes perfect

a We want to solve the given system of equations.

3=a * b^0 & (I) 75=a * b^2 & (II)

Notice that one of the factors in Equation I equals b^0. Powers with an exponent of 0 are equal to 1, so we can substitute b^0= 1. 3=a * 1 75=a * b^2 ⇒ a=3 & (I) 75=a * b^2 & (II) In the obtained system of equations at least one of the variables has a coefficient of 1. Therefore, we will approach its solution with the Substitution Method. When solving a system of equations using substitution, there are three steps.

Isolate a variable in one of the equations.
Substitute the expression for that variable into the other equation and solve.
Substitute this solution into one of the equations and solve for the value of the other variable.

For this exercise, a is already calculated in Equation I, so to find the value of b we can skip straight to substituting a=3 into the second equation.

a=3 75 = a * b^2

Substitute

(II):a= 3

a=3 75= 3 * b^2

DivEqn

(II): .LHS /3.=.RHS /3.

a=3 25=b^2

RearrangeEqn

(II): Rearrange equation

a=3 b^2=25

SqrtEqn

(II): sqrt(LHS)=sqrt(RHS)

a=3 b=± sqrt(25)

CalcRoot

(II): Calculate root

a=3 b=± 5

As we can see, the values a=3 and b= ± 5 make the given system of equations true. Thus, it has two solutions: a=3 and - 5, and a=3 and b=5.

b We want to solve the given system of equations.

18=a * b^2 & (I) 54=a * b^3 & (II)

When solving a system of equations using substitution, there are three steps.

Isolate a variable in one of the equations.
Substitute the expression for that variable into the other equation and solve.
Substitute this solution into one of the equations and solve for the value of the other variable.

Observing the given equations, it looks like it will be simplest to isolate a in the first equation.

18=a * b^2 54=a * b^3

▼

(I): Solve for a

DivEqn

(I): .LHS /b^2.=.RHS /b^2.

18b^2=a 54=a * b^3

RearrangeEqn

(I): Rearrange equation

a= 18b^2 54=a * b^3

Now that we have isolated a we can solve the system by substitution.

a= 18b^2 54=a * b^3