Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x+2=0
-
Equation 2x=0
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Equation (x-1)(-x-4)=0
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Equation x^3=x^2-7*x+7
- Express {x} in terms of y where:
- -15*x-19*y=2
- 4*x+4*y=13
- -4*x+14*y=-2
- 6*x+4*y=15
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Identical expressions
- 5x-3y=6z
- 5x minus 3y equally 6z
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Similar expressions
- z^8-6*z^4+9=0
- 2*x-y=5*x-3*y
- 4x+(-15x)-3y+3y=7+(-2)
- 5*x-3*y+63=0
- z^2+6*z+13=0
- 5x+3y=6z
- 2/3*((1/2)*z-(6/5))-4*((11/10)*z-2)=3*(1/6*z-3)+2*z+10
5x-3y=6z equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the linear equation:
Looking for similar summands in the left part:
Move the summands with the other variables
from left part to right part, we given:
$$5 x = 3 y + 6 z$$
Divide both parts of the equation by 5
We get the answer: x = 3*y/5 + 6*z/5
5*x-3*y = 6*z
Looking for similar summands in the left part:
-3*y + 5*x = 6*z
Move the summands with the other variables
from left part to right part, we given:
$$5 x = 3 y + 6 z$$
Divide both parts of the equation by 5
x = 3*y + 6*z / (5)
We get the answer: x = 3*y/5 + 6*z/5
The graph
Rapid solution
[src]
3*re(y) 6*re(z) /3*im(y) 6*im(z)\
x1 = ------- + ------- + I*|------- + -------|
5 5 \ 5 5 /
$$x_{1} = i \left(\frac{3 \operatorname{im}{\left(y\right)}}{5} + \frac{6 \operatorname{im}{\left(z\right)}}{5}\right) + \frac{3 \operatorname{re}{\left(y\right)}}{5} + \frac{6 \operatorname{re}{\left(z\right)}}{5}$$
x1 = i*(3*im(y)/5 + 6*im(z)/5) + 3*re(y)/5 + 6*re(z)/5
Sum and product of roots
[src]
sum
3*re(y) 6*re(z) /3*im(y) 6*im(z)\ ------- + ------- + I*|------- + -------| 5 5 \ 5 5 /
$$i \left(\frac{3 \operatorname{im}{\left(y\right)}}{5} + \frac{6 \operatorname{im}{\left(z\right)}}{5}\right) + \frac{3 \operatorname{re}{\left(y\right)}}{5} + \frac{6 \operatorname{re}{\left(z\right)}}{5}$$
=
3*re(y) 6*re(z) /3*im(y) 6*im(z)\ ------- + ------- + I*|------- + -------| 5 5 \ 5 5 /
$$i \left(\frac{3 \operatorname{im}{\left(y\right)}}{5} + \frac{6 \operatorname{im}{\left(z\right)}}{5}\right) + \frac{3 \operatorname{re}{\left(y\right)}}{5} + \frac{6 \operatorname{re}{\left(z\right)}}{5}$$
product
3*re(y) 6*re(z) /3*im(y) 6*im(z)\ ------- + ------- + I*|------- + -------| 5 5 \ 5 5 /
$$i \left(\frac{3 \operatorname{im}{\left(y\right)}}{5} + \frac{6 \operatorname{im}{\left(z\right)}}{5}\right) + \frac{3 \operatorname{re}{\left(y\right)}}{5} + \frac{6 \operatorname{re}{\left(z\right)}}{5}$$
=
3*re(y) 6*re(z) 3*I*(2*im(z) + im(y)) ------- + ------- + --------------------- 5 5 5
$$\frac{3 i \left(\operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(z\right)}\right)}{5} + \frac{3 \operatorname{re}{\left(y\right)}}{5} + \frac{6 \operatorname{re}{\left(z\right)}}{5}$$
3*re(y)/5 + 6*re(z)/5 + 3*i*(2*im(z) + im(y))/5