Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation -x^2-4*x-3=0
-
Equation 3x+3=-2-7x
-
Equation sin(-x)=0
-
Equation (x+3)^3=81*(x+3)
- Express {x} in terms of y where:
- 8*x-7*y=15
- 6*x+4*y=-13
- -3*x-12*y=-6
- 1*x-18*y=-19
-
Identical expressions
- 11x+12y+13z=14a+15b+16c
- 11x plus 12y plus 13z equally 14a plus 15b plus 16c
-
Similar expressions
- 11x-12y+13z=14a+15b+16c
- 11x+12y+13z=14a-15b+16c
- 11x+12y-13z=14a+15b+16c
- 11x+12y+13z=14a+15b-16c
11x+12y+13z=14a+15b+16c equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
11*x + 12*y + 13*z = 14*a + 15*b + 16*c
$$13 z + \left(11 x + 12 y\right) = 16 c + \left(14 a + 15 b\right)$$
Detail solution
Given the linear equation:
Looking for similar summands in the left part:
Looking for similar summands in the right part:
Move the summands with the other variables
from left part to right part, we given:
$$11 x + 13 z = 14 a + 15 b + 16 c - 12 y$$
Divide both parts of the equation by (11*x + 13*z)/x
We get the answer: x = -13*z/11 - 12*y/11 + 14*a/11 + 15*b/11 + 16*c/11
11*x+12*y+13*z = 14*a+15*b+16*c
Looking for similar summands in the left part:
11*x + 12*y + 13*z = 14*a+15*b+16*c
Looking for similar summands in the right part:
11*x + 12*y + 13*z = 14*a + 15*b + 16*c
Move the summands with the other variables
from left part to right part, we given:
$$11 x + 13 z = 14 a + 15 b + 16 c - 12 y$$
Divide both parts of the equation by (11*x + 13*z)/x
x = -12*y + 14*a + 15*b + 16*c / ((11*x + 13*z)/x)
We get the answer: x = -13*z/11 - 12*y/11 + 14*a/11 + 15*b/11 + 16*c/11
The graph
Rapid solution
[src]
13*re(z) 12*re(y) 14*re(a) 15*re(b) 16*re(c) / 13*im(z) 12*im(y) 14*im(a) 15*im(b) 16*im(c)\
x1 = - -------- - -------- + -------- + -------- + -------- + I*|- -------- - -------- + -------- + -------- + --------|
11 11 11 11 11 \ 11 11 11 11 11 /
$$x_{1} = i \left(\frac{14 \operatorname{im}{\left(a\right)}}{11} + \frac{15 \operatorname{im}{\left(b\right)}}{11} + \frac{16 \operatorname{im}{\left(c\right)}}{11} - \frac{12 \operatorname{im}{\left(y\right)}}{11} - \frac{13 \operatorname{im}{\left(z\right)}}{11}\right) + \frac{14 \operatorname{re}{\left(a\right)}}{11} + \frac{15 \operatorname{re}{\left(b\right)}}{11} + \frac{16 \operatorname{re}{\left(c\right)}}{11} - \frac{12 \operatorname{re}{\left(y\right)}}{11} - \frac{13 \operatorname{re}{\left(z\right)}}{11}$$
x1 = i*(14*im(a)/11 + 15*im(b)/11 + 16*im(c)/11 - 12*im(y)/11 - 13*im(z)/11) + 14*re(a)/11 + 15*re(b)/11 + 16*re(c)/11 - 12*re(y)/11 - 13*re(z)/11
Sum and product of roots
[src]
sum
13*re(z) 12*re(y) 14*re(a) 15*re(b) 16*re(c) / 13*im(z) 12*im(y) 14*im(a) 15*im(b) 16*im(c)\
- -------- - -------- + -------- + -------- + -------- + I*|- -------- - -------- + -------- + -------- + --------|
11 11 11 11 11 \ 11 11 11 11 11 /
$$i \left(\frac{14 \operatorname{im}{\left(a\right)}}{11} + \frac{15 \operatorname{im}{\left(b\right)}}{11} + \frac{16 \operatorname{im}{\left(c\right)}}{11} - \frac{12 \operatorname{im}{\left(y\right)}}{11} - \frac{13 \operatorname{im}{\left(z\right)}}{11}\right) + \frac{14 \operatorname{re}{\left(a\right)}}{11} + \frac{15 \operatorname{re}{\left(b\right)}}{11} + \frac{16 \operatorname{re}{\left(c\right)}}{11} - \frac{12 \operatorname{re}{\left(y\right)}}{11} - \frac{13 \operatorname{re}{\left(z\right)}}{11}$$
=
13*re(z) 12*re(y) 14*re(a) 15*re(b) 16*re(c) / 13*im(z) 12*im(y) 14*im(a) 15*im(b) 16*im(c)\
- -------- - -------- + -------- + -------- + -------- + I*|- -------- - -------- + -------- + -------- + --------|
11 11 11 11 11 \ 11 11 11 11 11 /
$$i \left(\frac{14 \operatorname{im}{\left(a\right)}}{11} + \frac{15 \operatorname{im}{\left(b\right)}}{11} + \frac{16 \operatorname{im}{\left(c\right)}}{11} - \frac{12 \operatorname{im}{\left(y\right)}}{11} - \frac{13 \operatorname{im}{\left(z\right)}}{11}\right) + \frac{14 \operatorname{re}{\left(a\right)}}{11} + \frac{15 \operatorname{re}{\left(b\right)}}{11} + \frac{16 \operatorname{re}{\left(c\right)}}{11} - \frac{12 \operatorname{re}{\left(y\right)}}{11} - \frac{13 \operatorname{re}{\left(z\right)}}{11}$$
product
13*re(z) 12*re(y) 14*re(a) 15*re(b) 16*re(c) / 13*im(z) 12*im(y) 14*im(a) 15*im(b) 16*im(c)\
- -------- - -------- + -------- + -------- + -------- + I*|- -------- - -------- + -------- + -------- + --------|
11 11 11 11 11 \ 11 11 11 11 11 /
$$i \left(\frac{14 \operatorname{im}{\left(a\right)}}{11} + \frac{15 \operatorname{im}{\left(b\right)}}{11} + \frac{16 \operatorname{im}{\left(c\right)}}{11} - \frac{12 \operatorname{im}{\left(y\right)}}{11} - \frac{13 \operatorname{im}{\left(z\right)}}{11}\right) + \frac{14 \operatorname{re}{\left(a\right)}}{11} + \frac{15 \operatorname{re}{\left(b\right)}}{11} + \frac{16 \operatorname{re}{\left(c\right)}}{11} - \frac{12 \operatorname{re}{\left(y\right)}}{11} - \frac{13 \operatorname{re}{\left(z\right)}}{11}$$
=
13*re(z) 12*re(y) 14*re(a) 15*re(b) 16*re(c) I*(-13*im(z) - 12*im(y) + 14*im(a) + 15*im(b) + 16*im(c))
- -------- - -------- + -------- + -------- + -------- + ---------------------------------------------------------
11 11 11 11 11 11
$$\frac{i \left(14 \operatorname{im}{\left(a\right)} + 15 \operatorname{im}{\left(b\right)} + 16 \operatorname{im}{\left(c\right)} - 12 \operatorname{im}{\left(y\right)} - 13 \operatorname{im}{\left(z\right)}\right)}{11} + \frac{14 \operatorname{re}{\left(a\right)}}{11} + \frac{15 \operatorname{re}{\left(b\right)}}{11} + \frac{16 \operatorname{re}{\left(c\right)}}{11} - \frac{12 \operatorname{re}{\left(y\right)}}{11} - \frac{13 \operatorname{re}{\left(z\right)}}{11}$$
-13*re(z)/11 - 12*re(y)/11 + 14*re(a)/11 + 15*re(b)/11 + 16*re(c)/11 + i*(-13*im(z) - 12*im(y) + 14*im(a) + 15*im(b) + 16*im(c))/11