Chapter 6.1, Problem 9LC

To determine

To conclude: about graphs of the given equations.

Answer to Problem 9LC

If two linear equations are true when $x=-2$ and $y=3$ , the graphs of both the linear equations intersect at this point.

Explanation of Solution

Given information : The two linear equations are true when $x=-2,y=3$

An equation is a statement that contains an equal symbol. It represents that the expressions on both the sides of $=$ are equal.

An equation in which degree of the variable is $1$ represents a linear equation.

(Degree refers to the highest power of the variable)

If an equation is satisfied by a point $\left(x_0,y_0\right)$ then the point $\left(x_0,y_0\right)$ is said to be a solution of the equation.

If each of the equations in a system of equations is satisfied by a point $\left(x_0,y_0\right)$ , the graphs of the equations in the given system of equations intersect at this point.

Therefore,

If two linear equations are true when $x=-2$ and $y=3$ , the graphs of both the linear equations intersect at this point.