Solve (c) Evaluate (3 3 ^ 1 -2 5 ^ 3 )(6 5 ^ 1 -4 3 ^ 2 ) (d) Solve (i) (ii) (5x - 6)/(3x + 2) = 2/3; 3m - (m + 1) = 6m + 1 | 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

$$\left. \begin{array} { l } { ( 3 ^ { 3 } - 2 ^ { 3 } ) ( 6 \frac { 1 } { 3 } - 2 ^ { 3 } ) } \\ { \quad } \\ { \quad \frac { 8 x - 4 } { 3 x + 1 } = \frac { 2 } { 3 } } \\ { \text { ( i \right.$$

Solve for x, y

$y = -\frac{95}{3} = -31\frac{2}{3} \approx -31.666666667$

Solution Steps

Consider the first equation. Variable $x$ cannot be equal to $-\frac{1}{3}$ since division by zero is not defined. Multiply both sides of the equation by $3\left(3x+1\right)$, the least common multiple of $3x+1,3$.

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

Use the distributive property to multiply $3$ by $8x-4$.

$$24x-12=2\left(3x+1\right)$$

Use the distributive property to multiply $2$ by $3x+1$.

$$24x-12=6x+2$$

Subtract $6x$ from both sides.

$$24x-12-6x=2$$

Combine $24x$ and $-6x$ to get $18x$.

$$18x-12=2$$

Add $12$ to both sides.

$$18x=2+12$$

Add $2$ and $12$ to get $14$.

$$18x=14$$

Divide both sides by $18$.

$$x=\frac{14}{18}$$

Reduce the fraction $\frac{14}{18}$ to lowest terms by extracting and canceling out $2$.

$$x=\frac{7}{9}$$

Consider the second equation. Calculate $3$ to the power of $3$ and get $27$.

$$y=\left(27-2^{3}\right)\left(\frac{6\times 3+1}{3}-2^{3}\right)$$

Calculate $2$ to the power of $3$ and get $8$.

$$y=\left(27-8\right)\left(\frac{6\times 3+1}{3}-2^{3}\right)$$

Subtract $8$ from $27$ to get $19$.

$$y=19\left(\frac{6\times 3+1}{3}-2^{3}\right)$$

Multiply $6$ and $3$ to get $18$.

$$y=19\left(\frac{18+1}{3}-2^{3}\right)$$

Add $18$ and $1$ to get $19$.

$$y=19\left(\frac{19}{3}-2^{3}\right)$$

Calculate $2$ to the power of $3$ and get $8$.

$$y=19\left(\frac{19}{3}-8\right)$$

Subtract $8$ from $\frac{19}{3}$ to get $-\frac{5}{3}$.

$$y=19\left(-\frac{5}{3}\right)$$

Multiply $19$ and $-\frac{5}{3}$ to get $-\frac{95}{3}$.

$$y=-\frac{95}{3}$$

The system is now solved.

$$x=\frac{7}{9}$$ $$y=-\frac{95}{3}$$