Math Exam prep

Question 1

How do you determine the number of solutions for a system of linear equations without solving it?

Answer 1

A: Compare the slopes and y-intercepts:

One solution: Different slopes.
No solution: Same slope, different y-intercepts.
Many solutions: Same slope and y-intercept.

Question 2

What are the steps to solve a system of linear equations using substitution?

Answer 2

1. Solve one equation for one variable.
2. Substitute this expression into the other equation.
3. Solve for the remaining variable.
4. Substitute back to find the other variable.

Question 3

How do you calculate the midpoint of a line segment joining points A(x1,y1) and 𝐵(𝑥2,𝑦2)
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Answer 3

The midpoint is (𝑥1+𝑥2, 𝑦1+𝑦2)

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Question 4

What are the characteristics of a system of linear equations with one solution?

Answer 4

The lines have different slopes.

Question 5

What does it mean when a system of linear equations has no solution?

Answer 5

The lines are parallel with the same slope but different y-intercepts.

Question 6

When does a system of linear equations have infinitely many solutions?

Answer 6

The lines are identical, having the same slope and y-intercept.

Question 7

How do you solve for the intersection point using Elimination?

Answer 7

1. Align the equations and eliminate one variable by adding or subtracting.
2. Solve for the remaining variable.
3. Back-substitute to find the other variable.

Question 8

How do you calculate the length of a line segment between two points?𝐴(𝑥1,𝑦1) and 𝐵(𝑥2,𝑦2)

Answer 8

Use the formula: √(𝑥2−𝑥1)²(𝑦2−𝑦1)²

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Question 9

How do you find the slope of a line segment?

Answer 9

Use the formula:
y₂-y₁
——-
x₂-y₁
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