Solve (x - y)/2022 + (x - 4)/2023 + (x - 3)/2024 = 3; x = 8 | 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

$$\frac{x-y}{2022}+\frac{x-4}{2023}+\frac{x-3}{2024}=3; x=8$$

Solve for x, y

$x=8$
$y = -\frac{12383986687}{2047276} = -6049\frac{14163}{2047276} \approx -6049.006917973$

Solution Steps

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

$$\frac{8-y}{2022}+\frac{8-4}{2023}+\frac{8-3}{2024}=3$$

Multiply both sides of the equation by $4139592072$, the least common multiple of $2022,2023,2024$.

$$2047276\left(8-y\right)+2046264\left(8-4\right)+2045253\left(8-3\right)=12418776216$$

Use the distributive property to multiply $2047276$ by $8-y$.

$$16378208-2047276y+2046264\left(8-4\right)+2045253\left(8-3\right)=12418776216$$

Subtract $4$ from $8$ to get $4$.

$$16378208-2047276y+2046264\times 4+2045253\left(8-3\right)=12418776216$$

Multiply $2046264$ and $4$ to get $8185056$.

$$16378208-2047276y+8185056+2045253\left(8-3\right)=12418776216$$

Add $16378208$ and $8185056$ to get $24563264$.

$$24563264-2047276y+2045253\left(8-3\right)=12418776216$$

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

$$24563264-2047276y+2045253\times 5=12418776216$$

Multiply $2045253$ and $5$ to get $10226265$.

$$24563264-2047276y+10226265=12418776216$$

Add $24563264$ and $10226265$ to get $34789529$.

$$34789529-2047276y=12418776216$$

Subtract $34789529$ from both sides.

$$-2047276y=12418776216-34789529$$

Subtract $34789529$ from $12418776216$ to get $12383986687$.

$$-2047276y=12383986687$$

Divide both sides by $-2047276$.

$$y=-\frac{12383986687}{2047276}$$

The system is now solved.

$$x=8$$ $$y=-\frac{12383986687}{2047276}$$