Solve \left\{ \begin{array} { l } { \frac { x + 1 } {

Question

Solve the system of equations

Solve using the substitution method

Solve using the elimination method

Solve using the Gauss-Jordan method

(x, y) = (2, 2)

Evaluate

{\frac{x + 1}{3} = \frac{y + 2}{4} \frac{x - 3}{4} - \frac{y - 3}{3} = \frac{1}{12}

Solve the equation for x

More Steps

{x = \frac{3 y + 2}{4} \frac{x - 3}{4} - \frac{y - 3}{3} = \frac{1}{12}

Substitute the given value of x into the equation \frac{x - 3}{4} - \frac{y - 3}{3} = \frac{1}{12}

\frac{\frac{3 y + 2}{4} - 3}{4} - \frac{y - 3}{3} = \frac{1}{12}

Simplify

More Steps

\frac{3 y - 10}{16} - \frac{y - 3}{3} = \frac{1}{12}

Multiply both sides of the equation by LCD

(\frac{3 y - 10}{16} - \frac{y - 3}{3}) \times 48 = \frac{1}{12} \times 48

Simplify the equation

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- 7 y + 18 = \frac{1}{12} \times 48

Simplify the equation

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- 7 y + 18 = 4

Move the constant to the right side

- 7 y = 4 - 18

Subtract the terms

- 7 y = - 14

Multiply both sides of the equation by - \frac{1}{7}

- 7 y (- \frac{1}{7}) = - 14 (- \frac{1}{7})

Multiply the numbers

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- 7 y (- \frac{1}{7}) = 2

Cancel out the greatest common factor - 7

y = 2

Substitute the given value of y into the equation x = \frac{3 y + 2}{4}

x = \frac{3 \times 2 + 2}{4}

Simplify the expression

x = 2

Calculate

{x = 2 y = 2

Check the solution

More Steps

{x = 2 y = 2

Solution

(x, y) = (2, 2)

Show Solution

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