Systems of Equations - Best Methods Guided Notes

When is the graphing method most suitable for solving systems of equations?

• When the system involves quadratic equations.

• When the coefficients of the variables are opposites.

• When one of the variables is already isolated.

• When both equations are in slope-intercept form and an estimated solution is acceptable.

What is the main disadvantage of the graphing method?

• It can only provide estimated solutions.

• It always provides the exact solution.

• It requires complex calculations.

• It cannot be used with linear equations.

How do you verify the solution obtained by graphing?

• By estimating the intersection point.

• Using a calculator.

• Algebraically verifying the solution.

• Graphing is always exact; no verification needed.

What does it mean when an equation is in 'slope-intercept' form?

• It is written as ax^2 + bx + c = 0.

• It is written as ax + by = c.

• It is written as y = mx + b.

• It is written as x = my + b.

In the substitution method, what condition makes it easier to apply?

• When the system cannot be graphed.

• When one of the variables is already isolated or can be easily isolated.

• When the variables have matching coefficients.

• When both equations are in standard form.

Which method is described as always working but sometimes being more complex than necessary?

• Matrix

• Elimination

• Substitution

• Graphing

Which method involves replacing a variable in one equation with its equivalent from another equation?

• Graphing

• Substitution

• Elimination

• Factoring

What is the primary reason to choose the elimination method over substitution?

• When the variables are aligned and have matching or opposite coefficients.

• When the system includes a quadratic equation.

• When the equations are in slope-intercept form.

• When it's impossible to isolate a variable.

What is the first step in the elimination method?

• Isolating a variable.

• Making the coefficients of one variable match or be opposites.

• Graphing both equations.

• Substituting one equation into the other.

When solving a system of equations, what does the solution represent?

• The maximum value of the system.

• The intersection point of the equations on a graph.

• The coefficients of the variables.

• The slope of the graph.