Solve {l}{3x/5-1/4=x-7x/10}{text{Solvefor}ytext{where}}{y=-1/5}

$$\left. \begin{array} { l } { \frac{3 x}{5} - \frac{1}{4} = x - \frac{7 x}{10} }\\ { \text{Solve for } y \text{ where} } \\ { y = -\frac{1}{5} } \end{array} \right.$$

Solve for x, y

$$y=-\frac{1}{5}=-0.2$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 20, the least common multiple of 5,4,10.

$$4\times 3x-5=20x-2\times 7x$$

Multiply 4 and 3 to get 12.

$$12x-5=20x-2\times 7x$$

Multiply -2 and 7 to get -14.

$$12x-5=20x-14x$$

Combine 20x and -14x to get 6x.

$$12x-5=6x$$

Subtract 6x from both sides.

$$12x-5-6x=0$$

Combine 12x and -6x to get 6x.

$$6x-5=0$$

Add 5 to both sides. Anything plus zero gives itself.

$$6x=5$$

Divide both sides by 6.

$$x=\frac{5}{6}$$

The system is now solved.

$$x=\frac{5}{6} y=-\frac{1}{5}$$