Chapter 9.6, Problem 4MRE

To determine

To find: the solution of each system using addition and subtraction method.

Answer to Problem 4MRE

The equation can be solved till $\frac{{\text{9b}}^{\text{2}}\text{+b-2}}{4\left(\text{3b+1}\right)}$ .

Explanation of Solution

Given:

  $\frac{{\text{9b}}^{\text{2}}\text{+b-2}}{\text{12b+4}}$ .

Concept used:

In the elimination method:

Either add or subtract equation to get an equation in one variable.

When the coefficients in one variable are opposites then add the equations to eliminate the variable and when the coefficients of one variable are equal and subtract the equation to eliminate a variable.

Calculation:

According to the given equation:

  $\frac{{\text{9b}}^{\text{2}}\text{+b-2}}{\text{12b+4}}$ .

The numerator is not factorable since ether are not two numbers that multiply to $\text{9}\left(-2\right)=-18$ and add to $1$ so leave the numerator as it is and in the denominator factor out the G.C.F of $4$ .

  $\frac{{\text{9b}}^{\text{2}}\text{+b-2}}{\text{12b+4}}=\frac{{\text{9b}}^{\text{2}}\text{+b-2}}{4\left(\text{3b+1}\right)}$ .

Hence, the equation can be solved till $\frac{{\text{9b}}^{\text{2}}\text{+b-2}}{4\left(\text{3b+1}\right)}$ .