Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 6*x^2+x-7=0
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Equation (x^2-9)^2+(x^2+x-6)^2=0
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Equation sin(2*x-pi/3)=0
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Equation x/(75/5)=60
- Express {x} in terms of y where:
- 16*x+12*y=-13
- -1*x+5*y=15
- -8*x+8*y=-6
- -19*x-18*y=-6
- Derivative of:
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-5
- -5
- Integral of d{x}:
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-5
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Identical expressions
- -3x+ five y+3z=-5
- minus 3x plus 5y plus 3z equally minus 5
- minus 3x plus five y plus 3z equally minus 5
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Similar expressions
- 3x+5y+3z=-5
- -3x+5y+3z=+5
- -3x+5y-3z=-5
- -3x-5y+3z=-5
-3x+5y+3z=-5 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:
$$- 3 x + 5 y = - 3 z - 5$$
Divide both parts of the equation by (-3*x + 5*y)/x
We get the answer: x = 5/3 + z + 5*y/3
-3*x+5*y+3*z = -5
Looking for similar summands in the left part:
-3*x + 3*z + 5*y = -5
Move the summands with the other variables
from left part to right part, we given:
$$- 3 x + 5 y = - 3 z - 5$$
Divide both parts of the equation by (-3*x + 5*y)/x
x = -5 - 3*z / ((-3*x + 5*y)/x)
We get the answer: x = 5/3 + z + 5*y/3
The graph
Rapid solution
[src]
5 5*re(y) /5*im(y) \
x1 = - + ------- + I*|------- + im(z)| + re(z)
3 3 \ 3 /
$$x_{1} = i \left(\frac{5 \operatorname{im}{\left(y\right)}}{3} + \operatorname{im}{\left(z\right)}\right) + \frac{5 \operatorname{re}{\left(y\right)}}{3} + \operatorname{re}{\left(z\right)} + \frac{5}{3}$$
x1 = i*(5*im(y)/3 + im(z)) + 5*re(y)/3 + re(z) + 5/3
Sum and product of roots
[src]
sum
5 5*re(y) /5*im(y) \ - + ------- + I*|------- + im(z)| + re(z) 3 3 \ 3 /
$$i \left(\frac{5 \operatorname{im}{\left(y\right)}}{3} + \operatorname{im}{\left(z\right)}\right) + \frac{5 \operatorname{re}{\left(y\right)}}{3} + \operatorname{re}{\left(z\right)} + \frac{5}{3}$$
=
5 5*re(y) /5*im(y) \ - + ------- + I*|------- + im(z)| + re(z) 3 3 \ 3 /
$$i \left(\frac{5 \operatorname{im}{\left(y\right)}}{3} + \operatorname{im}{\left(z\right)}\right) + \frac{5 \operatorname{re}{\left(y\right)}}{3} + \operatorname{re}{\left(z\right)} + \frac{5}{3}$$
product
5 5*re(y) /5*im(y) \ - + ------- + I*|------- + im(z)| + re(z) 3 3 \ 3 /
$$i \left(\frac{5 \operatorname{im}{\left(y\right)}}{3} + \operatorname{im}{\left(z\right)}\right) + \frac{5 \operatorname{re}{\left(y\right)}}{3} + \operatorname{re}{\left(z\right)} + \frac{5}{3}$$
=
5 5*re(y) /5*im(y) \ - + ------- + I*|------- + im(z)| + re(z) 3 3 \ 3 /
$$i \left(\frac{5 \operatorname{im}{\left(y\right)}}{3} + \operatorname{im}{\left(z\right)}\right) + \frac{5 \operatorname{re}{\left(y\right)}}{3} + \operatorname{re}{\left(z\right)} + \frac{5}{3}$$
5/3 + 5*re(y)/3 + i*(5*im(y)/3 + im(z)) + re(z)