3x+2y=4 equation

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3*x + 2*y = 4

$$3 x + 2 y = 4$$

Simplify

Detail solution

Given the linear equation:

3*x+2*y = 4

Looking for similar summands in the left part:

2*y + 3*x = 4

Move the summands with the other variables
from left part to right part, we given:
$$2 y = 4 - 3 x$$
Divide both parts of the equation by 2

y = 4 - 3*x / (2)

We get the answer: y = 2 - 3*x/2

The graph

Rapid solution [src]

         3*re(x)   3*I*im(x)
y1 = 2 - ------- - ---------
            2          2

$$y_{1} = - \frac{3 \operatorname{re}{\left(x\right)}}{2} - \frac{3 i \operatorname{im}{\left(x\right)}}{2} + 2$$

y1 = -3*re(x)/2 - 3*i*im(x)/2 + 2

Sum and product of roots [src]

sum

    3*re(x)   3*I*im(x)
2 - ------- - ---------
       2          2

$$- \frac{3 \operatorname{re}{\left(x\right)}}{2} - \frac{3 i \operatorname{im}{\left(x\right)}}{2} + 2$$

    3*re(x)   3*I*im(x)
2 - ------- - ---------
       2          2

$$- \frac{3 \operatorname{re}{\left(x\right)}}{2} - \frac{3 i \operatorname{im}{\left(x\right)}}{2} + 2$$

product

    3*re(x)   3*I*im(x)
2 - ------- - ---------
       2          2

$$- \frac{3 \operatorname{re}{\left(x\right)}}{2} - \frac{3 i \operatorname{im}{\left(x\right)}}{2} + 2$$

    3*re(x)   3*I*im(x)
2 - ------- - ---------
       2          2

$$- \frac{3 \operatorname{re}{\left(x\right)}}{2} - \frac{3 i \operatorname{im}{\left(x\right)}}{2} + 2$$

2 - 3*re(x)/2 - 3*i*im(x)/2