Q. 6

Question

If the lines that make up a system of two linear equations are coincident, then the system is __________ and the equations are ___________.

Step-by-Step Solution

Verified

Answer

If the lines that make up a system of two linear equations are coincident, then the system is consistent and the equations are dependent.

1Step 1. Given information.

If the lines that make up a system of two linear equations are coincident, then the system is __________ and the equations are ___________.

2Step 2. Determine the missing terms for the blanks.

Consistent and independent: A system of equations is consistent and independent if it has only one solution or two linear equations intersect each other only once.

Consistent and dependent: A system of equations is consistent and dependent if it has an infinite number of solutions or two linear equations are coincident.

By using the above definitions, it is clear that the required words for the blanks are consistent and dependent respectively.

3Step 3. Conclusion.

If the lines that make up a system of two linear equations are coincident, then the system is consistent and the equations are dependent.

Q. 5

Q. 7

Other exercises in this chapter

Q. 4

If a system of equations has one solution, the system is ________ and the equations are ________.

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Q. 5

If the solution to a system of two linear equations containing two unknowns is x=3, y=-2, then the lines intersect at the point _________.

View solution

Q. 7

Verify that the values of the variables listed are solutions of the system of equations.2x-y=55x+2y=8x=2, y=-1; (2,-1)

View solution

Q. 8

Verify that the values of the variables listed are solutions of the system of equations.3x+2y=2x-7y=-30x=-2, y=4;(-2,4)

View solution