Chapter 3, Problem 1PCT

Given the linear equation 4x –3y = 10, determine whether the ordered pair (1, –2) is a solution to the equation. Answer Yes or No.

To determine

Whether the ordered pair $\left(1,-2\right)$ satisfies the equation $4x-3y=10$ or not.

Answer to Problem 1PCT

Yes, the ordered pair $\left(1,-2\right)$ satisfies the equation $4x-3y=10$.

Explanation of Solution

Procedure used:

Step 1: Substitute the values of $x$ and $y$ in first equation and verify whether the equality holds.

Step 2: Repeat the procedure in step 1 for the second equation as well.

Step 3: If the equality holds in both step 1 and step 2, then conclude that the given ordered pair is a solution of the given system.

Calculation:

The given equation is $4x-3y=10$.

From the given ordered pair $\left(1,-2\right)$, it is observed that x coordinate is $1$ and y coordinate is $-2$.

Substitute $x=1$ and $y=-2$ in equation $4x-3y=10$.

$\begin{array}{l}4x-3y=10\\ 4\left(1\right)-3\left(-2\right)\stackrel{?}{=}10\\ 4+6\stackrel{?}{=}10\\ 10=10\end{array}$

Since left hand side is equal to right hand side, the statement $y=-3x+5$ is true.

Yes, the ordered pair $\left(1,-2\right)$ satisfies the equation $4x-3y=10$.