Solve y = 24/7; (12x)/5 - (7x)/3 + 5 = (3x)/10 * 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

$$y=\frac{24}{7}; \frac{12x}{5}-\frac{7x}{3}+5=\frac{3x}{10}*1$$

Solve for y, x

$x = \frac{150}{7} = 21\frac{3}{7} \approx 21.428571429$
$y = \frac{24}{7} = 3\frac{3}{7} \approx 3.428571429$

Solution Steps

Consider the second equation. Multiply both sides of the equation by $30$, the least common multiple of $5,3,10$.

$$6\times 12x-10\times 7x+150=3\times 3x\times 1$$

Multiply $6$ and $12$ to get $72$.

$$72x-10\times 7x+150=3\times 3x\times 1$$

Multiply $-10$ and $7$ to get $-70$.

$$72x-70x+150=3\times 3x\times 1$$

Combine $72x$ and $-70x$ to get $2x$.

$$2x+150=3\times 3x\times 1$$

Multiply $3$ and $3$ to get $9$.

$$2x+150=9x\times 1$$

Multiply $9$ and $1$ to get $9$.

$$2x+150=9x$$

Subtract $9x$ from both sides.

$$2x+150-9x=0$$

Combine $2x$ and $-9x$ to get $-7x$.

$$-7x+150=0$$

Subtract $150$ from both sides. Anything subtracted from zero gives its negation.

$$-7x=-150$$

Divide both sides by $-7$.

$$x=\frac{-150}{-7}$$

Fraction $\frac{-150}{-7}$ can be simplified to $\frac{150}{7}$ by removing the negative sign from both the numerator and the denominator.

$$x=\frac{150}{7}$$

The system is now solved.

$$y=\frac{24}{7}$$ $$x=\frac{150}{7}$$