MENU
❌
Home
Math Forum/Help
Problem Solver
Practice
Algebra
Geometry
Tests
College Math
History
Games
MAIN MENU
1 Grade
Adding and subtracting up to 10
Comparing numbers up to 10
Adding and subtracting up to 20
Addition and Subtraction within 20
2 Grade
Adding and Subtracting up to 100
Addition and Subtraction within 20
3 Grade
Addition and Subtraction within 1000
Multiplication up to 5
Multiplication Table
Rounding
Dividing
Addition, Multiplication, Division
Perimeter
4 Grade
Adding and Subtracting
Addition, Multiplication, Division
Equivalent Fractions
Divisibility by 2, 3, 4, 5, 9
Area of Squares and Rectangles
Fractions
Equivalent Fractions
Least Common Multiple
Adding and Subtracting
Fraction Multiplication and Division
Operations
Mixed Numbers
Decimals
Expressions
6 Grade
Percents
Signed Numbers
The Coordinate Plane
Equations
Expressions
Polynomials
Polynomial Vocabulary
Symplifying Expressions
Polynomial Expressions
Factoring
7 Grade
Angles
Inequalities
Linear Functions
8 Grade
Congurence of Triangles
Linear Functions
Systems of equations
Slope
Parametric Linear Equations
Word Problems
Exponents
Roots
Quadratic Equations
Quadratic Inequalities
Rational Inequalities
Vieta's Formulas
Progressions
Arithmetic Progressions
Geometric Progression
Progressions
Number Sequences
Reciprocal Equations
Logarithms
Logarithmic Expressions
Logarithmic Equations
Trigonometry
Trigonometry
Identities
Trigonometry
Trigonometric Inequalities
Extremal value problems
Numbers Classification
Geometry
Intercept Theorem
Slope
Law of Sines
Law of Cosines
Vectors
Probability
Limits of Functions
Properties of Triangles
Pythagorean Theorem
Matrices
Complex Numbers
Inverse Trigonometric Functions
Analytic Geometry
Analytic Geometry
Circle
Parabola
Ellipse
Conic sections
Polar coordinates
Integrals
Integrals
Integration by Parts
Trigonometric Substitutions
Differential Equations
Home
Practice
Parametric Linear Equations
Easy
Normal
Difficult
Parametric Linear Equations: Problems with Solutions
Problem 1
Find the value of
a
, for which the equation [tex]ax=1[/tex] has no solutions.
Solution:
If we can divide by
a
, there is always the solution [tex]x=\frac{1}{a}[/tex]. Let's check the case where we cannot divide by
a
, in other words
a=0
. We get the equation [tex]0x=1[/tex], which has no solutions. Therefore the answer to the problem is
a=0
.
Problem 2
Find the value of the real parameter
a
, for which the equation [tex](a-2)x=(a-2)^2[/tex] has any
x
for solution.
Solution:
For an equation to have any
x
as solution, it must be of the form
0x=0
. Which means that [tex](a-2)=(a-2)^2=0[/tex], or
a=2
.
Problem 3
Find the value of the parameter
b
, for which the equation
0x=b-7
has at least one solution
x
.
Solution:
For any
x
, the value of the left side is zero. We get
b-7=0
, or
b=7
. By substituting, we get
0x=0
, which has infinitely many solutions.
Problem 4
Solve the equation for
a=3
:
[tex]x+a=2a+1[/tex]
Solution:
We subtract
a
from both sides of the equation to get
[tex]x=a+1[/tex]. We substitute
a=3
:
[tex]x=3+1=4[/tex]
Problem 5
Find the value of
a
, for which the equation
[tex]\frac{1}{a+5}x=a+7[/tex] is not defined.
Solution:
If the equation is to be not defined, then a denominator must be zero. The only denominator is [tex]a+5[/tex], so we get [tex]a=-5[/tex]
Problem 6
Solve the equation [tex](a^3+1)x=109+a[/tex] for [tex]a=3[/tex]
Solution:
We directly substitute:
[tex](3^3+1)x=109+3[/tex]
[tex]28x=112[/tex]
[tex]x=4[/tex]
Problem 7
Solve the equation [tex](a^4-250)x=a^3+2[/tex] for
a=4
.
Solution:
We substitute:
[tex](4^4-250)x=4^3+2[/tex]
[tex](256-250)x=64+2[/tex]
[tex]6x=66[/tex]
[tex]x=11[/tex]
Problem 8
Solve the parametric linear equation [tex](a^3+9)x=237+10a[/tex] for
a=-2
.
Solution:
We substitute:
[tex]((-2)^3+9)x=237+10\cdot(-2)[/tex]
[tex](-8+9)x=237-20[/tex]
[tex]x=217[/tex]
Problem 9
Solve the equation [tex]5ax=85[/tex] for
a=17
.
Solution:
We directly substitute:
[tex]5\cdot17x=85[/tex]
[tex]85x=85[/tex]
[tex]x=1[/tex]
Easy
Normal
Difficult
Submit a problem on this page.
Problem text:
Solution:
Answer:
Your name(if you would like to be published):
E-mail(you will be notified when the problem is published)
Notes
: use [tex][/tex] (as in the forum if you would like to use latex).
Correct:
Wrong:
Unsolved problems:
Contact email:
Follow us on
Twitter
Facebook
Author
Copyright © 2005 - 2021.