Solve Systems Algebraically

The video tutorial explains linear equations in slope-intercept and standard forms, and how to graph them. It covers the possibilities of intersecting, parallel, and identical lines, leading to one, no, or infinite solutions. The elimination method is detailed for solving systems of equations, including examples of systems with no solutions and infinite solutions. The tutorial also addresses solving complex systems using the least common multiple (LCM) to eliminate variables.

What are the possible outcomes when graphing two linear equations on the same coordinate plane?

• Only one solution

• One solution, no solution, or infinitely many solutions

• No solution or infinitely many solutions

• Only infinitely many solutions

In the elimination method, what must be true about the coefficients of the variable you want to eliminate?

• They must be different and positive

• They must be equal and positive

• They must be equal and opposite in sign

• They must be different and negative

What does it mean when two linear equations have the same slope but different y-intercepts?

• The lines are perpendicular

• The lines are the same

• The lines intersect at one point

• The lines are parallel and have no solutions

What is the result when both variables cancel out and the equation becomes 0 = 3?

• The system is inconsistent

• The system has no solutions

• The system has one solution

• The system has infinitely many solutions

What does it indicate when the elimination method results in the equation 0 = 0?

• The system has infinitely many solutions

• The system has no solutions

• The system has one solution

• The system is inconsistent

How do you solve a system of equations when the coefficients are not the same?

• Multiply both equations by zero

• Find the least common multiple of the coefficients

• Add the equations directly

• Subtract the equations

What is the point of intersection for the system of equations -7X - 8Y = 9 and -4X + 9Y = -22?

• (1, -2)

• (-1, 2)

• (2, -1)

• (-2, 1)