Question

the graphical representation of a consistent and independent system of equations will show the lines. the term for a set of two or more equations with the same variables is called a. when solving $2x + 3y = 12$ and $4x - 3y = 6$ using elimination, the solution for $x$ is. the process of finding the values of variables that satisfy two or more equations simultaneously is called systems of equations.

Explanation:

First Question:

A consistent and independent system of linear equations has exactly one solution. Graphically, this means the two lines intersect at a single point, so they are intersecting (not parallel or coinciding).

By definition, a set of two or more equations with the same variables is called a system of equations.

Step1: Add the two equations

We have the system:
$$2x + 3y = 12$$
$$4x - 3y = 6$$
Adding them eliminates \(y\): \((2x + 3y)+(4x - 3y)=12 + 6\)
Simplify: \(6x=18\)

Step2: Solve for \(x\)

Divide both sides by 6: \(x=\frac{18}{6}=3\)

Answer:

intersecting at one point

Second Question: