Solve Solve by elimination method 3/(x - 2) + 4/(y + 1) = 1; 7/(2x - 4) - 25/(3y + 3) - 3 | 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

$$\left. \begin{array} { l } { \frac { 3 } { x - 2 } + \frac { 4 } { y + 1 } = 1 } \\ { \frac { 7 } { 24 - 4 } - \frac { 25 } { 9 y + 3 \right.$$

Solve for x

$x=-\frac{5y-3}{3-y}$
$y\neq -1\text{ and }y\neq 3$

Steps for Solving Linear Equation

Variable $x$ cannot be equal to $2$ since division by zero is not defined. Multiply both sides of the equation by $\left(x-2\right)\left(y+1\right)$, the least common multiple of $x-2,y+1$.

$$\left(y+1\right)\times 3+\left(x-2\right)\times 4=\left(x-2\right)\left(y+1\right)$$

Use the distributive property to multiply $y+1$ by $3$.

$$3y+3+\left(x-2\right)\times 4=\left(x-2\right)\left(y+1\right)$$

Use the distributive property to multiply $x-2$ by $4$.

$$3y+3+4x-8=\left(x-2\right)\left(y+1\right)$$

Subtract $8$ from $3$ to get $-5$.

$$3y-5+4x=\left(x-2\right)\left(y+1\right)$$

Use the distributive property to multiply $x-2$ by $y+1$.

$$3y-5+4x=xy+x-2y-2$$

Subtract $xy$ from both sides.

$$3y-5+4x-xy=x-2y-2$$

Subtract $x$ from both sides.

$$3y-5+4x-xy-x=-2y-2$$

Combine $4x$ and $-x$ to get $3x$.

$$3y-5+3x-xy=-2y-2$$

Subtract $3y$ from both sides.

$$-5+3x-xy=-2y-2-3y$$

Combine $-2y$ and $-3y$ to get $-5y$.

$$-5+3x-xy=-5y-2$$

Add $5$ to both sides.

$$3x-xy=-5y-2+5$$

Add $-2$ and $5$ to get $3$.

$$3x-xy=-5y+3$$

Combine all terms containing $x$.

$$\left(3-y\right)x=-5y+3$$

The equation is in standard form.

$$\left(3-y\right)x=3-5y$$

Divide both sides by $-y+3$.

$$\frac{\left(3-y\right)x}{3-y}=\frac{3-5y}{3-y}$$

Dividing by $-y+3$ undoes the multiplication by $-y+3$.

$$x=\frac{3-5y}{3-y}$$

Variable $x$ cannot be equal to $2$.

$$x=\frac{3-5y}{3-y}\text{, }x\neq 2$$