Solve a=b+1 b=c+1 a+b+c=21

Question

Solve the system of equations

Solve using the substitution method

Solve using the elimination method

Solve using the Gauss-Jordan method

(a, b, c) = (21, \frac{21}{2}, - \frac{21}{4})

Alternative Form

(a, b, c) = (21, 10.5, - 5.25)

Evaluate

⎩ ⎨ ⎧ a = b + 1 \times b b + 1 \times b = c + 1 \times a + b + c c + 1 \times a + b + c = 21

Calculate

More Steps

⎩ ⎨ ⎧ a = 2 b b + 1 \times b = c + 1 \times a + b + c c + 1 \times a + b + c = 21

Cancel equal terms on both sides of the expression

⎩ ⎨ ⎧ a = 2 b 1 \times b = c + 1 \times a + c c + 1 \times a + b + c = 21

Calculate

More Steps

⎩ ⎨ ⎧ a = 2 b b = 2 c + a c + 1 \times a + b + c = 21

Calculate

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⎩ ⎨ ⎧ a = 2 b b = 2 c + a 2 c + a + b = 21

Substitute the given value of a into the equation {b = 2 c + a 2 c + a + b = 21

{b = 2 c + 2 b 2 c + 2 b + b = 21

Simplify

{b = 2 c + 2 b 2 c + 3 b = 21

Solve the equation for b

More Steps

{b = - 2 c 2 c + 3 b = 21

Substitute the given value of b into the equation 2 c + 3 b = 21

2 c + 3 (- 2 c) = 21

Simplify

More Steps

- 4 c = 21

Change the signs on both sides of the equation

4 c = - 21

Divide both sides

\frac{4 c}{4} = \frac{- 21}{4}

Divide the numbers

c = \frac{- 21}{4}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

c = - \frac{21}{4}

Substitute the given value of c into the equation b = - 2 c

b = - 2 (- \frac{21}{4})

Calculate

b = \frac{21}{2}

Substitute the given value of b into the equation a = 2 b

a = 2 \times \frac{21}{2}

Calculate

a = 21

Calculate

⎩ ⎨ ⎧ a = 21 b = \frac{21}{2} c = - \frac{21}{4}

Check the solution

More Steps

⎩ ⎨ ⎧ a = 21 b = \frac{21}{2} c = - \frac{21}{4}

Solution

(a, b, c) = (21, \frac{21}{2}, - \frac{21}{4})

Alternative Form

(a, b, c) = (21, 10.5, - 5.25)

Show Solution