Chapter 8, Problem 1MCT

Determine which of the following ordered pairs satisfy each system of equations.

$\begin{array}{l}4x+3y=-1\\ x-2y=8\end{array}$

a. $\left(-1,1\right)$

b. $\left(2,-3\right)$

To determine

To find:

Which of the ordered pairs satisfy teach of the system of equations?

Answer to Problem 1MCT

Ordered pair $b.\left(2,-3\right)$ satisfies the system of equations.

Explanation of Solution

Given:

  $\begin{array}{l}4x+3y=-1\\ x-2y=8\\ a.\left(-1,1\right)\\ b.\left(2,-3\right)\end{array}$

Calculation:

We have been given the system of equations

  $\begin{array}{l}4x+3y=-\mathrm{1...}\left(i\right)\\ x-2y=\mathrm{8...}\left(ii\right)\end{array}$

For the ordered pair $a.\left(-1,1\right)$

Substitute $x=-1,y=1$ in the equation $\left(i\right)$

  $\begin{array}{l}4\cdot 1+3\cdot 1=-1\\ 4+3=-1\\ 7=-1\end{array}$

We got a false result since, $7\ne -1$

Hence, the ordered pair $\left(-1,1\right)$ doesn't satisfy the system of equations.

Similarly, we check for the other ordered pair.

For the ordered pair $\left(2,-3\right)$

Substitute $x=2,y=-3$ in the equation $\left(i\right)$

  $\begin{array}{l}4\cdot 2+3\cdot \left(-3\right)=-1\\ 8-9=-1\\ -1=-1\Rightarrow \text{True}\end{array}$

Substitute $x=2,y=-3$ in the equation $\left(ii\right)$

  $\begin{array}{l}x-2y=8\\ 2-2\left(-3\right)=8\\ 2+6=8\\ 8=8\Rightarrow \text{True}\end{array}$

We got true results for both the equations.

Hence, the ordered pair $b.\left(2,-3\right)$ satisfies the system of equations.

Conclusion:

The ordered pair $b.\left(2,-3\right)$ satisfies the system of equations.