Solve a=2b-10 a=40 b

Question

Solve the system of equations

Solve using the substitution method

Solve using the elimination method

Solve using the Gauss-Jordan method

(a, b) = (0, 0)

Evaluate

{a = 2 b - 10 a 2 b - 10 a = 40 b

Solve the equation for a

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Evaluate

a = 2 b - 10 a

Move the variable to the left side

a + 10 a = 2 b

Add the terms

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Evaluate

a + 10 a

Collect like terms by calculating the sum or difference of their coefficients

(1 + 10) a

Add the numbers

11 a

11 a = 2 b

Divide both sides

\frac{11 a}{11} = \frac{2 b}{11}

Divide the numbers

a = \frac{2 b}{11}

{a = \frac{2 b}{11} 2 b - 10 a = 40 b

Substitute the given value of a into the equation 2 b - 10 a = 40 b

2 b - 10 \times \frac{2 b}{11} = 40 b

Multiply the terms

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Evaluate

2 b - 10 \times \frac{2 b}{11}

Multiply the terms

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Multiply the terms

10 \times \frac{2 b}{11}

Multiply the terms

\frac{10 \times 2 b}{11}

Multiply the terms

\frac{20 b}{11}

2 b - \frac{20 b}{11}

2 b - \frac{20 b}{11} = 40 b

Multiply both sides of the equation by LCD

(2 b - \frac{20 b}{11}) \times 11 = 40 b \times 11

Simplify the equation

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Evaluate

(2 b - \frac{20 b}{11}) \times 11

Apply the distributive property

2 b \times 11 - \frac{20 b}{11} \times 11

Simplify

2 b \times 11 - 20 b

Multiply the numbers

22 b - 20 b

Collect like terms by calculating the sum or difference of their coefficients

(22 - 20) b

Subtract the numbers

2 b

2 b = 40 b \times 11

Simplify the equation

2 b = 440 b

Add or subtract both sides

2 b - 440 b = 0

Subtract the terms

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Evaluate

2 b - 440 b

Collect like terms by calculating the sum or difference of their coefficients

(2 - 440) b

Subtract the numbers

- 438 b

- 438 b = 0

Change the signs on both sides of the equation

438 b = 0

Rewrite the expression

b = 0

Substitute the given value of b into the equation a = \frac{2 b}{11}

a = \frac{2 \times 0}{11}

Calculate

a = 0

Calculate

{a = 0 b = 0

Check the solution

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Check the solution

{0 = 2 \times 0 - 10 \times 0 2 \times 0 - 10 \times 0 = 40 \times 0

Simplify

{0 = 0 0 = 0

Evaluate

true

{a = 0 b = 0

Solution

(a, b) = (0, 0)

Show Solution

Relationship between lines

Neither parallel nor perpendicular

Evaluate

a = 2 b - 10 a, 2 b - 10 a = 40 b

Write the equation in slope-intercept form

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Evaluate

a = 2 b - 10 a

Move the expression to the right side

0 = 2 b - 11 a

Move the expression to the left side

- 2 b = - 11 a

Divide both sides

b = \frac{11}{2} a

b = \frac{11}{2} a, 2 b - 10 a = 40 b

Write the equation in slope-intercept form

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Evaluate

2 b - 10 a = 40 b

Move the expression to the right side

2 b = 40 b + 10 a

Move the expression to the left side

- 38 b = 10 a

Divide both sides

b = - \frac{5}{19} a

b = \frac{11}{2} a, b = - \frac{5}{19} a

Since the line is in slope-intercept form, the coefficient \frac{11}{2} is the slope of the line

\frac{11}{2}, b = - \frac{5}{19} a

Since the line is in slope-intercept form, the coefficient - \frac{5}{19} is the slope of the line

\frac{11}{2}, - \frac{5}{19}

The slopes are different, so the lines aren't parallel. We'll multiply the slopes to check their relationship

\frac{11}{2} (- \frac{5}{19})

Multiplying or dividing an odd number of negative terms equals a negative

- \frac{11}{2} \times \frac{5}{19}

To multiply the fractions,multiply the numerators and denominators separately

- \frac{11 \times 5}{2 \times 19}

Multiply the numbers

- \frac{55}{2 \times 19}

Multiply the numbers

- \frac{55}{38}

Solution

Neither parallel nor perpendicular

Show Solution