Solving Systems of Equations

The video tutorial reviews solving systems of equations using graphing, substitution, and matrix methods. It demonstrates solving problems with Desmos and the TI-84 calculator, highlighting the advantages and limitations of each method. The tutorial emphasizes understanding where graphs intersect and the practical applications of these techniques in higher-level math and finance.

What is the solution to the system of equations where the first line has a slope of -5/3 and intercept 3, and the second line has a slope of 1/3 and intercept -30?

• (1, 1)

• (0, 0)

• (-3, 2)

• (3, -2)

Which method can be used to solve a system of equations if graphing is not precise?

• Substitution

• Differentiation

• Elimination

• Integration

In the substitution method, if y = 4x + 3 and y = -x - 2, what is the value of x?

• -1

• 0

• 1

• 2

What is the y-value when x = -1 in the system where y = 4x + 3 and y = -x - 2?

• 0

• -1

• 2

• 1

What is the first step in setting up a system of equations for solving using a matrix on the TI-84?

• Find the determinant

• Use substitution

• Rewrite equations in standard form

• Graph the equations

How many rows and columns are in the matrix used to solve a system of two equations with two variables on the TI-84?

• 2x2

• 3x3

• 2x3

• 3x2

What is the solution to the system of equations: -7x - 2y = -13 and x - 2y = 11?

• (3, -4)

• (2, -3)

• (1, 1)

• (0, 0)

Which tool can be used to verify the solution of a system of equations graphically?

• Python

• Desmos

• TI-84

• Excel

What is the advantage of using matrices to solve systems of equations?

• It requires less data

• It is faster

• It is easier to understand

• It is more accurate

In which quadrant do the lines intersect for the system: -7x - 2y = -13 and x - 2y = 11?

• First

• Second

• Third

• Fourth