Solve using the substitution method of { x + y + z = 6, 2x - y + z = 5, x + 2y - z = 3 }

\left(x,y,z\right) = \left(\frac{15}{7},\frac{11}{7},\frac{16}{7}\right)

Solve using the elimination method of { x + y + z = 6, 2x - y + z = 5, x + 2y - z = 3 }

\left(x,y,z\right) = \left(\frac{15}{7},\frac{11}{7},\frac{16}{7}\right)

\left(x,y,z\right) = \left(\frac{15}{7},\frac{11}{7},\frac{16}{7}\right)

\left(x,y,z\right) = \left(\frac{15}{7},\frac{11}{7},\frac{16}{7}\right)

Question :

Solve using the substitution method

Solve using the elimination method

Solve using the Gauss-Jordan method

(x, y, z) = (\frac{15}{7}, \frac{11}{7}, \frac{16}{7})

Alternative Form

(x, y, z) = (2. \dot{1} 4285 \dot{7}, 1. \dot{5} 7142 \dot{8}, 2. \dot{2} 8571 \dot{4})

Evaluate

⎩ ⎨ ⎧ x + y + z = 6 2 x - y + z = 5 x + 2 y - z = 3

Solve the equation for x

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⎩ ⎨ ⎧ x = 6 - y - z 2 x - y + z = 5 x + 2 y - z = 3

Substitute the given value of x into the equation {2 x - y + z = 5 x + 2 y - z = 3

{2 (6 - y - z) - y + z = 5 6 - y - z + 2 y - z = 3

Simplify

More Steps

{12 - 3 y - z = 5 6 - y - z + 2 y - z = 3

Simplify

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{12 - 3 y - z = 5 6 + y - 2 z = 3

Solve the equation for z

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{z = 7 - 3 y 6 + y - 2 z = 3

Substitute the given value of z into the equation 6 + y - 2 z = 3

6 + y - 2 (7 - 3 y) = 3

Simplify

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- 8 + 7 y = 3

Move the constant to the right-hand side and change its sign

7 y = 3 + 8

Add the numbers

7 y = 11

Divide both sides

\frac{7 y}{7} = \frac{11}{7}

Divide the numbers

y = \frac{11}{7}

Substitute the given value of y into the equation z = 7 - 3 y

z = 7 - 3 \times \frac{11}{7}

Calculate

z = \frac{16}{7}

Substitute the given values of y, z into the equation x = 6 - y - z

x = 6 - \frac{11}{7} - \frac{16}{7}

Calculate

x = \frac{15}{7}

Calculate

⎩ ⎨ ⎧ x = \frac{15}{7} y = \frac{11}{7} z = \frac{16}{7}

Check the solution

More Steps

⎩ ⎨ ⎧ x = \frac{15}{7} y = \frac{11}{7} z = \frac{16}{7}

Solution

(x, y, z) = (\frac{15}{7}, \frac{11}{7}, \frac{16}{7})

Alternative Form

(x, y, z) = (2. \dot{1} 4285 \dot{7}, 1. \dot{5} 7142 \dot{8}, 2. \dot{2} 8571 \dot{4})

Show Solution