Solve numjen. = x y * 5 2 + 2 3 = -7 12 | 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

$$= \frac { x } { y } \times \frac { 5 } { 2 } + \frac { 2 } { 3 } = \frac { - 7 } { 12 }$$

Solve for x

$x=-\frac{y}{2}$
$y\neq 0$

Steps for Solving Linear Equation

Multiply both sides of the equation by $12y$, the least common multiple of $y,2,3,12$.

$$12x\times \frac{5}{2}+12y\times \frac{2}{3}=y\left(-7\right)$$

Multiply $12$ and $\frac{5}{2}$ to get $30$.

$$30x+12y\times \frac{2}{3}=y\left(-7\right)$$

Multiply $12$ and $\frac{2}{3}$ to get $8$.

$$30x+8y=y\left(-7\right)$$

Subtract $8y$ from both sides.

$$30x=y\left(-7\right)-8y$$

Combine $y\left(-7\right)$ and $-8y$ to get $-15y$.

$$30x=-15y$$

Divide both sides by $30$.

$$\frac{30x}{30}=-\frac{15y}{30}$$

Dividing by $30$ undoes the multiplication by $30$.

$$x=-\frac{15y}{30}$$

Divide $-15y$ by $30$.

$$x=-\frac{y}{2}$$

Solve for y

$y=-2x$
$x\neq 0$

Steps for Solving Linear Equation

Variable $y$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $12y$, the least common multiple of $y,2,3,12$.

$$12x\times \frac{5}{2}+12y\times \frac{2}{3}=y\left(-7\right)$$

Multiply $12$ and $\frac{5}{2}$ to get $30$.

$$30x+12y\times \frac{2}{3}=y\left(-7\right)$$

Multiply $12$ and $\frac{2}{3}$ to get $8$.

$$30x+8y=y\left(-7\right)$$

Subtract $y\left(-7\right)$ from both sides.

$$30x+8y-y\left(-7\right)=0$$

Combine $8y$ and $-y\left(-7\right)$ to get $15y$.

$$30x+15y=0$$

Subtract $30x$ from both sides. Anything subtracted from zero gives its negation.

$$15y=-30x$$

Divide both sides by $15$.

$$\frac{15y}{15}=-\frac{30x}{15}$$

Dividing by $15$ undoes the multiplication by $15$.

$$y=-\frac{30x}{15}$$

Divide $-30x$ by $15$.

$$y=-2x$$

Variable $y$ cannot be equal to $0$.

$$y=-2x\text{, }y\neq 0$$