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

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Type your math problem... \left\{ \begin{array} { l } { \frac { x + 1 } { 3 } = \frac { y + 2 } { 4 } } \\ { \frac { x - 3 } { 4 } - \frac { y - 3 } { 3 } = \frac { 1 } { 12 } } \end{array} \right.

Question

Solve the system of equations

Solve using the substitution method

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Solve using the elimination method

Solve using the Gauss-Jordan method

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(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

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{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

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\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 numbers

- 7 y = - 14

Change the signs on both sides of the equation

7 y = 14

Divide both sides

\frac{7 y}{7} = \frac{14}{7}

Divide the numbers

y = \frac{14}{7}

Divide the numbers

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

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{x = 2 y = 2

Solution

(x, y) = (2, 2)

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