Match the terms to their definition. 1. consistent equations 2. dependent equations 3. equivalent equations 4. inconsistent equations 5. independent equations 6. no solution 7. one solution a common point known as the point of intersection $$ (x, y) $$; the solution, $$ (x, y) $$ is an independent and consistent solution $$ \square $$ a system of linear equations that do not rely on each other for the algebraic or graphic form of the equation $$ \square $$ a set of parallel lines that will never share a point of intersection; considered to be an inconsistent solution (fempty set") $$ \square $$ equations having all common solutions $$ \square $$ a system of linear equations that do not contain any common points $$ \square $$ a system of linear equations that rely on each other for the algebraic or graphic form of the equation $$ \square $$ a system of linear equations that contain at least one common point

Question

UpStudy AI · Accepted Answer

Let's match the terms to their definitions step by step:

1. **Consistent equations**: A system of linear equations that contain at least one common point.
   - Match: $$ \square $$ a system of linear equations that contain at least one common point

2. **Dependent equations**: A system of linear equations that rely on each other for the algebraic or graphic form of the equation.
   - Match: $$ \square $$ a system of linear equations that rely on each other for the algebraic or graphic form of the equation

3. **Equivalent equations**: Equations having all common solutions.
   - Match: $$ \square $$ equations having all common solutions

4. **Inconsistent equations**: A set of parallel lines that will never share a point of intersection; considered to be an inconsistent solution (empty set).
   - Match: $$ \square $$ a system of linear equations that do not contain any common points

5. **Independent equations**: A system of linear equations that do not rely on each other for the algebraic or graphic form of the equation.
   - Match: $$ \square $$ a system of linear equations that do not rely on each other for the algebraic or graphic form of the equation

6. **No solution**: A system of linear equations that do not contain any common points.
   - Match: $$ \square $$ a system of linear equations that do not contain any common points

7. **One solution**: A common point known as the point of intersection $$ (x, y) $$; the solution, $$ (x, y) $$ is an independent and consistent solution.
   - Match: $$ \square $$ a common point known as the point of intersection $$ (x, y) $$; the solution, $$ (x, y) $$ is an independent and consistent solution

Now, let's summarize the matches:

1. Consistent equations - $$ \square $$ a system of linear equations that contain at least one common point
2. Dependent equations - $$ \square $$ a system of linear equations that rely on each other for the algebraic or graphic form of the equation
3. Equivalent equations - $$ \square $$ equations having all common solutions
4. Inconsistent equations - $$ \square $$ a set of parallel lines that will never share a point of intersection; considered to be an inconsistent solution (empty set)
5. Independent equations - $$ \square $$ a system of linear equations that do not rely on each other for the algebraic or graphic form of the equation
6. No solution - $$ \square $$ a system of linear equations that do not contain any common points
7. One solution - $$ \square $$ a common point known as the point of intersection $$ (x, y) $$; the solution, $$ (x, y) $$ is an independent and consistent solution
1. Consistent equations - a system of linear equations that contain at least one common point 2. Dependent equations - a system of linear equations that rely on each other for the algebraic or graphic form of the equation 3. Equivalent equations - equations having all common solutions 4. Inconsistent equations - a set of parallel lines that will never share a point of intersection; considered to be an inconsistent solution (empty set) 5. Independent equations - a system of linear equations that do not rely on each other for the algebraic or graphic form of the equation 6. No solution - a system of linear equations that do not contain any common points 7. One solution - a common point known as the point of intersection $$ (x, y) $$; the solution, $$ (x, y) $$ is an independent and consistent solution

Upstudy AI Solution

Answer

Solution

Extra Insights

Related Questions

Latest Algebra Questions