Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^2+11*x+30=0
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Equation (-2-4t-1)²+(0+2t-1)²+(2+5t)²=9
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Equation (|3*x-9|)-(|x+2|)=7
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Equation k^2+3*k-4=0
- Express {x} in terms of y where:
- -17*x-8*y=-8
- 12*x-15*y=0
- -20*x-17*y=13
- -3*x-8*y=-18
- Sum of series:
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-1
- Integral of d{x}:
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-1
- Derivative of:
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-1
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Identical expressions
- one /(2x-y)=- one
- 1 divide by (2x minus y) equally minus 1
- one divide by (2x minus y) equally minus one
- 1/2x-y=-1
- 1 divide by (2x-y)=-1
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Similar expressions
- 1/(2x+y)=-1
- (3/(x+y-1))+(1/(2*x-y+3))+(7/5)=0
- 1/(2x-y)=+1
1/(2x-y)=-1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$\frac{1}{2 x - y} = -1$$
Use proportions rule:
From a1/b1 = a2/b2 should a1*b2 = a2*b1,
In this case
so we get the equation
$$-1 = 2 x - y$$
$$-1 = 2 x - y$$
Looking for similar summands in the right part:
Move free summands (without x)
from left part to right part, we given:
$$0 = 2 x - y + 1$$
Divide both parts of the equation by 0
We get the answer: x = -1/2 + y/2
$$\frac{1}{2 x - y} = -1$$
Use proportions rule:
From a1/b1 = a2/b2 should a1*b2 = a2*b1,
In this case
a1 = 1
b1 = -y + 2*x
a2 = 1
b2 = -1
so we get the equation
$$-1 = 2 x - y$$
$$-1 = 2 x - y$$
Looking for similar summands in the right part:
-1 = -y + 2*x
Move free summands (without x)
from left part to right part, we given:
$$0 = 2 x - y + 1$$
Divide both parts of the equation by 0
x = 1 - y + 2*x / (0)
We get the answer: x = -1/2 + y/2
The graph
Rapid solution
[src]
1 re(y) I*im(y)
x1 = - - + ----- + -------
2 2 2
$$x_{1} = \frac{\operatorname{re}{\left(y\right)}}{2} + \frac{i \operatorname{im}{\left(y\right)}}{2} - \frac{1}{2}$$
x1 = re(y)/2 + i*im(y)/2 - 1/2
Sum and product of roots
[src]
sum
1 re(y) I*im(y) - - + ----- + ------- 2 2 2
$$\frac{\operatorname{re}{\left(y\right)}}{2} + \frac{i \operatorname{im}{\left(y\right)}}{2} - \frac{1}{2}$$
=
1 re(y) I*im(y) - - + ----- + ------- 2 2 2
$$\frac{\operatorname{re}{\left(y\right)}}{2} + \frac{i \operatorname{im}{\left(y\right)}}{2} - \frac{1}{2}$$
product
1 re(y) I*im(y) - - + ----- + ------- 2 2 2
$$\frac{\operatorname{re}{\left(y\right)}}{2} + \frac{i \operatorname{im}{\left(y\right)}}{2} - \frac{1}{2}$$
=
1 re(y) I*im(y) - - + ----- + ------- 2 2 2
$$\frac{\operatorname{re}{\left(y\right)}}{2} + \frac{i \operatorname{im}{\left(y\right)}}{2} - \frac{1}{2}$$
-1/2 + re(y)/2 + i*im(y)/2