Chapter 5.2, Problem 12E

To determine

To solve and check: The give equation

Answer to Problem 12E

Here, the solution of the system is the ordered pair $\left(x,y\right)=\left(3,22\right)$

Explanation of Solution

Given:

Calculation:

  $\begin{array}{l}-5x+3y=51\\ y=10x-8\end{array}$

Substitute the given value of $y$ into the equation $-5x+3y=51$

  $-5x+3\left(10-8\right)=51$

Solve the equation for $x$

  $\boxed{x=3}$

Substitute the given of $x$ into the equation $y=10x-8$

  $y=10\times 3-8$

Solve the equation for $y$

  $\boxed{y=22}$

The solution of the system is the ordered pair $\left(x,y\right)=\left(3,22\right)$

Check if the ordered pair is the solution of the system of equations

  $\begin{array}{l}-5\times 3+3\times 22=51\\ 22=10\times 3-8\end{array}$

Simplify the equalities

  51=51✓

  22=22✓

Since all of equalities are true, the ordered pair is the solution of the system $\left(x,y\right)=\left(3,22\right)$

Conclusion:

Therefore, the solution of the system is the ordered pair $\left(x,y\right)=\left(3,22\right)$