Mister Exam
Other calculators
-
How to use it?
- Equation:
- Equation a*x=b
-
Equation 2-3(2+3x)=14
-
Equation x^2-x+8=0
-
Equation 2^x=7
- Express {x} in terms of y where:
- 8*x-4*y=10
- -17*x-5*y=-20
- 2*x+19*y=-7
- -4*x+7*y=-16
- Derivative of:
- a*x
- Integral of d{x}:
- a*x
- Limit of the function:
- a*x
-
Identical expressions
- a*x=b
- a multiply by x equally b
- ax=b
-
Similar expressions
- ax+3y=5
- ax^2+bx+c=0
- ax+b=c
a*x=b equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the linear equation:
Divide both parts of the equation by a
We get the answer: x = b/a
a*x = b
Divide both parts of the equation by a
x = b / (a)
We get the answer: x = b/a
The solution of the parametric equation
Given the equation with a parameter:
$$a x = b$$
Коэффициент при x равен
$$a$$
then possible cases for a :
$$a < 0$$
$$a = 0$$
Consider all cases in more detail:
With
$$a < 0$$
the equation
$$- b - x = 0$$
its solution
$$x = - b$$
With
$$a = 0$$
the equation
$$- b = 0$$
its solution
$$a x = b$$
Коэффициент при x равен
$$a$$
then possible cases for a :
$$a < 0$$
$$a = 0$$
Consider all cases in more detail:
With
$$a < 0$$
the equation
$$- b - x = 0$$
its solution
$$x = - b$$
With
$$a = 0$$
the equation
$$- b = 0$$
its solution
The graph
Sum and product of roots
[src]
sum
/b\ /b\
I*im|-| + re|-|
\a/ \a/
$$\operatorname{re}{\left(\frac{b}{a}\right)} + i \operatorname{im}{\left(\frac{b}{a}\right)}$$
=
/b\ /b\
I*im|-| + re|-|
\a/ \a/
$$\operatorname{re}{\left(\frac{b}{a}\right)} + i \operatorname{im}{\left(\frac{b}{a}\right)}$$
product
/b\ /b\
I*im|-| + re|-|
\a/ \a/
$$\operatorname{re}{\left(\frac{b}{a}\right)} + i \operatorname{im}{\left(\frac{b}{a}\right)}$$
=
/b\ /b\
I*im|-| + re|-|
\a/ \a/
$$\operatorname{re}{\left(\frac{b}{a}\right)} + i \operatorname{im}{\left(\frac{b}{a}\right)}$$
i*im(b/a) + re(b/a)
Rapid solution
[src]
/b\ /b\
x1 = I*im|-| + re|-|
\a/ \a/
$$x_{1} = \operatorname{re}{\left(\frac{b}{a}\right)} + i \operatorname{im}{\left(\frac{b}{a}\right)}$$
x1 = re(b/a) + i*im(b/a)