Question

consider the system of linear equations 2y equals x + 10

3 y equals 3x + 15which statement about the system are true

Answer 1

Answer: the system has one solution which is x = 0, y = 5.

Explanation:

The pair of equations given constitute a system of two equations with two variables.

A system of linear equations may have a single solution, no solution (parallel lines) or infinite solutions (same line).

To find the solution or determine whether the system has one or infinite solutions, you may manipulate the equations.

This is the original systeym as given:

• 2y = x + 10
• 3y = 3x + 15.

Multiply the first equation by 3 and the second equation by 2:

• 6y = 3x + 30
• 6y = 6x + 30

Subtract the first equation from the second:

• 0 = 3x
• ⇒ x = 0

Substitute x = 0 in any of the original equations to find y:

• 2y = 0 + 10
• 2y = 10
• y = 10 / 2
• y = 5

Hence, the system has one solution which is x = 0, y = 5.