Chapter 3, Problem 1RE

To determine

Whether the provided ordered pair $\left(4,2\right)$ is a solution to the system of equation $2x-5y=-2,3x+4y=4$.

Answer to Problem 1RE

Solution:

The ordered pair $\left(4,2\right)$ is not the solution of the provided system of equations $2x-5y=-2,3x+4y=4$.

Explanation of Solution

Given:

An ordered pair is $\left(4,2\right)$ and system of equation is

$\begin{array}{l}2x-5y=-2\\ 3x+4y=4\end{array}$

Explanation:

To check whether $\left(4,2\right)$ is a solution of the system or not, put $\left(4,2\right)$ in the first equation which is, $2x-5y=-2$

Put $x=4,y=2$

$\begin{array}{c}2\left(4\right)-5\left(2\right)=-2\\ 8-10=-2\\ -2=-2\end{array}$

Which is true.

So, $\left(4,2\right)$ satisfies the first equation, $2x-5y=-2$.

Now, put $\left(4,2\right)$ in the second equation which is $3x+4y=4$,

Put $x=4,y=2$

$\begin{array}{c}3\left(4\right)+4\left(2\right)=2\\ 12+8=2\\ 20=2\end{array}$

Which is not true.

So, $\left(4,2\right)$ does not satisfies the second equation, $3x+4y=4$.

Thus, $\left(4,2\right)$ is not the solution of the provided system.

Hence, the ordered pair $\left(4,2\right)$ is not the solution of the provided system of equations $2x-5y=-2,3x+4y=4$.