Name: Exercises on 3&#215;3 Systems of Equations
Brand: Superprof
SKU: SP-RB-00015705
Rating: 5 (2 reviews)

Chapters

Review of the General Formula
Quadratic Equation Exercises

Test your knowledge of second-degree equations with our excellent equations! Make sure to practice frequently and reach out to a Superprof tutor if you need additional help, to make sure you get an A+ on your next assignment.

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Review of the General Formula

To solve the proposed exercises, we’ll use the general formula for quadratic equations:

$\text{[math]}$

This formula is used to solve any second-degree equation of the form:

$\text{[math]}$ where $\text{[math]}$

Using this method is very simple — we just need to set the equation equal to zero and substitute the values of a, b, and c into the formula.

When solving a quadratic equation, three scenarios are possible:

There are two values for the variable x that satisfy the equation.
There is only one solution.
The solution does not belong to the set of real numbers.

Quadratic Equation Exercises

Score:

$\text{[math]}$

Solution

1 We identify the values of a, b and c

$\text{[math]}$

2 We substitute in the general formula and solve

$\text{[math]}$

3 The equation has two distinct real solutions

$\text{[math]}$

Solution

1 We identify the values of a, b and c

$\text{[math]}$

2 We substitute in the general formula and solve

$\text{[math]}$

3 The equation has two distinct real solutions

$\text{[math]}$

Solution

1 We identify the values of a, b and c

$\text{[math]}$

2 We substitute in the general formula and solve

$\text{[math]}$

3 The equation has no solution in the real numbers

$\text{[math]}$

Solution

1 We identify the values of a, b and c

$\text{[math]}$

2 We substitute in the general formula and solve

$\text{[math]}$

3 The equation has no solution in the real numbers

$\text{[math]}$

Solution

1 We identify the values of a, b and c

$\text{[math]}$

2 We substitute in the general formula and solve

$\text{[math]}$

3 The equation has two equal real solutions

$\text{[math]}$

Solution

1 We identify the values of a, b and c

$\text{[math]}$

2 We substitute in the general formula and solve

$\text{[math]}$

3 The equation has two distinct real solutions

$\text{[math]}$

Solution

1 We identify the values of a, b and c

$\text{[math]}$

2 We substitute in the general formula and solve

$\text{[math]}$

3 The equation has two distinct real solutions

$\text{[math]}$

Solution

1 We identify the values of a, b and c

$\text{[math]}$

2 We substitute in the general formula and solve

$\text{[math]}$

3 The equation has only one real solution

$\text{[math]}$

Solution

1 We identify the values of a, b and c

$\text{[math]}$

2 We substitute in the general formula and solve

$\text{[math]}$

3 The equation has no solution in the real numbers.

$\text{[math]}$

Solution

1 We identify the values of a, b and c

$\text{[math]}$

2 We substitute in the general formula and solve

$\text{[math]}$

3 The equation has only one real solution.

$\text{[math]}$

Solution

1 We move all terms to one side of the equation to have it in the form $\text{[math]}$

$\text{[math]}$

2 We identify the values of a, b and c

$\text{[math]}$

3 We substitute in the general formula and solve

$\text{[math]}$

4 The equation has only one real solution.

$\text{[math]}$

Solution

1 We solve the binomial squared

$\text{[math]}$

2 We move all terms to one side and group them to write the equation in the form $\text{[math]}$

$\text{[math]}$

3 We identify the values of a, b and c

$\text{[math]}$

4 We substitute in the general formula and solve

$\text{[math]}$

5 The equation has two real solutions.

$\text{[math]}$

Solution

1 In this case, we can divide both sides of the equation by 7 to simplify it

$\text{[math]}$

2 We identify the values of a, b and c

$\text{[math]}$

3 We substitute in the general formula and solve

$\text{[math]}$

4 The equation has two real solutions.

$\text{[math]}$

Solution

1 We multiply both sides by −1 to obtain an equivalent equation with a > 0

$\text{[math]}$

2 The equation has no real solutions

$\text{[math]}$

Solution

1 We use the distributive property to operate the parenthesis and obtain:

$\text{[math]}$

2 We operate and move everything to the first member

$\text{[math]}$

3 We identify the values of a, b and c

$\text{[math]}$

4 We substitute in the general formula and solve

$\text{[math]}$

5 The equation has two real solutions.

$\text{[math]}$

Solution

1 We identify the values of a, b and c

$\text{[math]}$

2 We substitute in the general formula and solve

$\text{[math]}$

3 The equation has two distinct real solutions

$\text{[math]}$

Solution

1 We solve the binomial squared

$\text{[math]}$

2 We move all terms to one side and group them to write the equation in the form $\text{[math]}$

$\text{[math]}$

3 We divide both sides of the equation by 2 to simplify it

$\text{[math]}$

4 We identify the values of a, b and c

$\text{[math]}$

5 We substitute in the general formula and solve

$\text{[math]}$

6 The equation has two real solutions.

$\text{[math]}$

Solution

1 We identify the values of a, b and c

$\text{[math]}$

2 We substitute in the general formula and solve

$\text{[math]}$

3 The equation has two distinct real solutions

$\text{[math]}$

Solution

1 We identify the values of a, b and c

$\text{[math]}$

2 We substitute in the general formula and solve

$\text{[math]}$

3 The equation has two distinct real solutions

$\text{[math]}$

Solution

1 We multiply the first member of the equation by 6, and the last by 2 to eliminate the denominator (6), and thus we obtain:

$\text{[math]}$

2 We identify the values of a, b and c

$\text{[math]}$

3 We substitute in the general formula and solve

$\text{[math]}$

4 The equation has two real solutions.

$\text{[math]}$

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Agostina Babbo

Agostina Babbo is an English and Italian to Spanish translator and writer, specializing in product localization, legal content for tech, and team sports—particularly handball and e-sports. With a degree in Public Translation from the University of Buenos Aires and a Master's in Translation and New Technologies from ISTRAD/Universidad de Madrid, she brings both linguistic expertise and technical insight to her work.

Exercises with Second-Degree Equations

Review of the General Formula

Quadratic Equation Exercises

What Are First-Degree Equations?

Quadratic Equations: Solved Exercises

Solved Exercises: First-Degree Equations

First-Degree Equation Problems

Exercises on 3×3 Systems of Equations

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Exercises with Second-Degree Equations

Review of the General Formula

Quadratic Equation Exercises

Theory

What Are First-Degree Equations?

Other Exercises

Quadratic Equations: Solved Exercises

Solved Exercises: First-Degree Equations

First-Degree Equation Problems

Exercises on 3×3 Systems of Equations

Cancel reply