Solve each system of equations.6.r−3s+t=43r−6s+9t=54r−9s+10t=9

Q6. - Algebra 2 | StudyQuestionHub

Solve each system of equations.

$\begin{array}{l} r - 3 s + t = 4 \\ 3 r - 6 s + 9 t = 5 \\ 4 r - 9 s + 10 t = 9 \end{array}$

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Answer

The solution has infinitely many solutions.

1Step-1 –Using elimination to obtain two equations in two variables

Given system of equations are

$\begin{array}{l} r - 3 s + t = 4 \\ 3 r - 6 s + 9 t = 5 \\ 4 r - 9 s + 10 t = 9 \end{array}$

Multiplying first equation by $3$ and subtracting with the second equation, we get

$\begin{array}{l} - 12 s + 9 s + 4 t - 10 t = 16 - 9 \\ - 3 s - 6 t = 7 \end{array}$

2Step-2 –Solving the system of two equations in two variables

System of equations with two variables are

$\begin{array}{l} - 3 s - 6 t = 7 \\ - 3 s - 6 t = 7 \end{array}$

Therefore, the equation $- 3 s - 6 t = 7$ has infinitely many solutions.

3Step-3 –Evaluating the value of r

Since, $s$ and $t$ has infinitely many values and so $r$ has many values.