Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x+7*4=40
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Equation -x^3+4*x^2+4*x-16=0
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Equation x/7=6
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Equation 2x-cosx=0
- Express {x} in terms of y where:
- 13*x-12*y=10
- -12*x-19*y=16
- 4*x-7*y=11
- 18*x-11*y=13
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Identical expressions
- five (x-4y+2c)= zero
- 5(x minus 4y plus 2c) equally 0
- five (x minus 4y plus 2c) equally zero
- 5x-4y+2c=0
- 5(x-4y+2c)=O
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Similar expressions
- 5(x-4y-2c)=0
- 5(x+4y+2c)=0
5(x-4y+2c)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the linear equation:
Expand brackets in the left part
Looking for similar summands in the left part:
Move the summands with the other variables
from left part to right part, we given:
$$10 c + 5 x = 20 y$$
Divide both parts of the equation by (5*x + 10*c)/x
We get the answer: x = -2*c + 4*y
5*(x-4*y+2*c) = 0
Expand brackets in the left part
5*x-5*4*y+5*2*c = 0
Looking for similar summands in the left part:
-20*y + 5*x + 10*c = 0
Move the summands with the other variables
from left part to right part, we given:
$$10 c + 5 x = 20 y$$
Divide both parts of the equation by (5*x + 10*c)/x
x = 20*y / ((5*x + 10*c)/x)
We get the answer: x = -2*c + 4*y
The graph
Rapid solution
[src]
x1 = -2*re(c) + 4*re(y) + I*(-2*im(c) + 4*im(y))
$$x_{1} = i \left(- 2 \operatorname{im}{\left(c\right)} + 4 \operatorname{im}{\left(y\right)}\right) - 2 \operatorname{re}{\left(c\right)} + 4 \operatorname{re}{\left(y\right)}$$
x1 = i*(-2*im(c) + 4*im(y)) - 2*re(c) + 4*re(y)
Sum and product of roots
[src]
sum
-2*re(c) + 4*re(y) + I*(-2*im(c) + 4*im(y))
$$i \left(- 2 \operatorname{im}{\left(c\right)} + 4 \operatorname{im}{\left(y\right)}\right) - 2 \operatorname{re}{\left(c\right)} + 4 \operatorname{re}{\left(y\right)}$$
=
-2*re(c) + 4*re(y) + I*(-2*im(c) + 4*im(y))
$$i \left(- 2 \operatorname{im}{\left(c\right)} + 4 \operatorname{im}{\left(y\right)}\right) - 2 \operatorname{re}{\left(c\right)} + 4 \operatorname{re}{\left(y\right)}$$
product
-2*re(c) + 4*re(y) + I*(-2*im(c) + 4*im(y))
$$i \left(- 2 \operatorname{im}{\left(c\right)} + 4 \operatorname{im}{\left(y\right)}\right) - 2 \operatorname{re}{\left(c\right)} + 4 \operatorname{re}{\left(y\right)}$$
=
-2*re(c) + 4*re(y) + 2*I*(-im(c) + 2*im(y))
$$2 i \left(- \operatorname{im}{\left(c\right)} + 2 \operatorname{im}{\left(y\right)}\right) - 2 \operatorname{re}{\left(c\right)} + 4 \operatorname{re}{\left(y\right)}$$
-2*re(c) + 4*re(y) + 2*i*(-im(c) + 2*im(y))