Question

Solve the given linear system of equations:68r12+18One solution:No solutionInfinite number of solutionsQuestion Help: Video MessageInstructorCheck Answer

Answer 1

Given the equations:

8x - 6y = 6 ...........................1

-212x + 9y = 18.......................2

Let's use substitution method to solve this.

Using equation 1:

8x - 6y = 6

Add 6y to both sides:

8x - 6y + 6y = 6 + 6y

8x = 6 + 6y

Divide through by 8:

$\begin{gathered} \frac{8x}{8}=\frac{6}{8}+\frac{6y}{8} \\ \\ x\text{ = }\frac{3}{4}+\frac{3}{4}y\ldots\ldots\ldots\ldots\ldots\ldots\ldots.3 \end{gathered}$

Substitute equation 3 into equation 1:

$\begin{gathered} 8(\frac{3}{4}+\frac{3}{4}y)\text{ - 6y = 6} \\ \\ 6\text{ + 6y - 6y = 6} \\ \\ 6\text{ = 6} \end{gathered}$

6 = 6

Since the right side of the equation equals the left side, the system has infinitely many solutions.

ANSWER:

Infinite number of solutions