Solve y+x(-6=105(x-2)(y-4) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$y+x(-6=105(x-2)(y-4)$$

Solve for x

$x=-\frac{211y-846}{421-105y}$
$y\neq \frac{421}{105}$

Steps for Solving Linear Equation

Use the distributive property to multiply $105$ by $x-2$.

$$y+x-6=\left(105x-210\right)\left(y-4\right)$$

Use the distributive property to multiply $105x-210$ by $y-4$.

$$y+x-6=105xy-420x-210y+840$$

Subtract $105xy$ from both sides.

$$y+x-6-105xy=-420x-210y+840$$

Add $420x$ to both sides.

$$y+x-6-105xy+420x=-210y+840$$

Combine $x$ and $420x$ to get $421x$.

$$y+421x-6-105xy=-210y+840$$

Subtract $y$ from both sides.

$$421x-6-105xy=-210y+840-y$$

Combine $-210y$ and $-y$ to get $-211y$.

$$421x-6-105xy=-211y+840$$

Add $6$ to both sides.

$$421x-105xy=-211y+840+6$$

Add $840$ and $6$ to get $846$.

$$421x-105xy=-211y+846$$

Combine all terms containing $x$.

$$\left(421-105y\right)x=-211y+846$$

The equation is in standard form.

$$\left(421-105y\right)x=846-211y$$

Divide both sides by $421-105y$.

$$\frac{\left(421-105y\right)x}{421-105y}=\frac{846-211y}{421-105y}$$

Dividing by $421-105y$ undoes the multiplication by $421-105y$.

$$x=\frac{846-211y}{421-105y}$$

Solve for y

$y=-\frac{421x-846}{211-105x}$
$x\neq \frac{211}{105}$

Steps for Solving Linear Equation

Use the distributive property to multiply $105$ by $x-2$.

$$y+x-6=\left(105x-210\right)\left(y-4\right)$$

Use the distributive property to multiply $105x-210$ by $y-4$.

$$y+x-6=105xy-420x-210y+840$$

Subtract $105xy$ from both sides.

$$y+x-6-105xy=-420x-210y+840$$

Add $210y$ to both sides.

$$y+x-6-105xy+210y=-420x+840$$

Combine $y$ and $210y$ to get $211y$.

$$211y+x-6-105xy=-420x+840$$

Subtract $x$ from both sides.

$$211y-6-105xy=-420x+840-x$$

Combine $-420x$ and $-x$ to get $-421x$.

$$211y-6-105xy=-421x+840$$

Add $6$ to both sides.

$$211y-105xy=-421x+840+6$$

Add $840$ and $6$ to get $846$.

$$211y-105xy=-421x+846$$

Combine all terms containing $y$.

$$\left(211-105x\right)y=-421x+846$$

The equation is in standard form.

$$\left(211-105x\right)y=846-421x$$

Divide both sides by $211-105x$.

$$\frac{\left(211-105x\right)y}{211-105x}=\frac{846-421x}{211-105x}$$

Dividing by $211-105x$ undoes the multiplication by $211-105x$.

$$y=\frac{846-421x}{211-105x}$$