Question

In the following exercises, determine if the following points are solutions to the given system of equations.

$\left\{\begin{array}{l}2x-6y=0\\ 3x-4y=5\end{array}\right.$

Short answer

The point $(-6,2)$satisfies the equation so it is a solution to the system of equation and $(-3,4)$doesn't satisfy so it is not a solution to the system of equation

Step-by-step solution

Step 1. Given information.

The system of equations$\left\{\begin{array}{l}2x-6y=0\\ 3x-4y=5\end{array}\right.$

Substituting the values.

The equation is,$\left\{\begin{array}{l}2x-6y=0\\ 3x-4y=5\end{array}\right.$, substituting the values, we get

$\begin{array}{r}2x-6y=0\\ 2\left(3\right)-6\left(1\right)=0\\ 6-6=0\\ 0=0\end{array}$

Substituting for equation

Substituting for $3x-4y=5$, we get

$\begin{array}{r}3x-4y=5\\ 3\left(3\right)-4\left(1\right)=5\\ 9-4=5\\ 5=5\end{array}$

Check for (-3,4)

Substituting, we get

$$\begin{gathered} 2(-3)-6(-4)=-6+24 \\ =18 \end{gathered}$$

$$\begin{gathered} 3(-3)-4\left(4\right)=-9-16 \\ =-25 \end{gathered}$$

So it is not a solution to the system of equations