Solve {l}{3x-4y-(2x-7)=0}{5(x-1)-(2x-1)=0}

$$\left\{ \begin{array} { l } { 3 x - 4 y - ( 2 x - 7 ) = 0 } \\ { 5 ( x - 1 ) - ( 2 x - 1 ) = 0 } \end{array} \right.$$

Solve for x, y

$$x = \frac{4}{3} = 1\frac{1}{3} \approx 1.333333333$$

$$y = \frac{25}{12} = 2\frac{1}{12} \approx 2.083333333$$

Solution Steps

Consider the second equation. Use the distributive property to multiply 5 by x-1.

$$5x-5-\left(2x-1\right)=0$$

To find the opposite of 2x-1, find the opposite of each term.

$$5x-5-2x+1=0$$

Combine 5x and -2x to get 3x.

$$3x-5+1=0$$

Add -5 and 1 to get -4.

$$3x-4=0$$

Add 4 to both sides. Anything plus zero gives itself.

$$3x=4$$

Divide both sides by 3.

$$x=\frac{4}{3}$$

Consider the first equation. Insert the known values of variables into the equation.

$$3\times \frac{4}{3}-4y-\left(2\times \frac{4}{3}-7\right)=0$$

Multiply 3 and \frac{4}{3} to get 4.

$$4-4y-\left(2\times \frac{4}{3}-7\right)=0$$

Multiply 2 and \frac{4}{3} to get \frac{8}{3}.

$$4-4y-\left(\frac{8}{3}-7\right)=0$$

Subtract 7 from \frac{8}{3} to get -\frac{13}{3}.

$$4-4y-\left(-\frac{13}{3}\right)=0$$

Multiply -1 and -\frac{13}{3} to get \frac{13}{3}.

$$4-4y+\frac{13}{3}=0$$

Add 4 and \frac{13}{3} to get \frac{25}{3}.

$$\frac{25}{3}-4y=0$$

Subtract \frac{25}{3} from both sides. Anything subtracted from zero gives its negation.

$$-4y=-\frac{25}{3}$$

Divide both sides by -4.

$$y=\frac{-\frac{25}{3}}{-4}$$

Express \frac{-\frac{25}{3}}{-4} as a single fraction.

$$y=\frac{-25}{3\left(-4\right)}$$

Multiply 3 and -4 to get -12.

$$y=\frac{-25}{-12}$$

Fraction \frac{-25}{-12} can be simplified to \frac{25}{12} by removing the negative sign from both the numerator and the denominator.

$$y=\frac{25}{12}$$

The system is now solved.

$$x=\frac{4}{3} y=\frac{25}{12}$$