Solve 11s - 4a = 102 8s - 6a = 86

Question

Solve the system of equations

Solve using the substitution method

Solve using the elimination method

Solve using the Gauss-Jordan method

(a, s) = (- \frac{43731}{2023}, - \frac{86}{2023})

Alternative Form

(a, s) \approx (- 21.616906, - 0.042511)

Evaluate

{11 s - 4 a = 1028 s - 6 a 1028 s - 6 a = 86

Solve the equation for a

More Steps

Evaluate

11 s - 4 a = 1028 s - 6 a

Move the expression to the left side

11 s - 4 a + 6 a = 1028 s

Move the expression to the right side

- 4 a + 6 a = 1028 s - 11 s

Add and subtract

More Steps

Evaluate

- 4 a + 6 a

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

(- 4 + 6) a

Add the numbers

2 a

2 a = 1028 s - 11 s

Add and subtract

More Steps

Evaluate

1028 s - 11 s

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

(1028 - 11) s

Subtract the numbers

1017 s

2 a = 1017 s

Divide both sides

\frac{2 a}{2} = \frac{1017 s}{2}

Divide the numbers

a = \frac{1017 s}{2}

{a = \frac{1017 s}{2} 1028 s - 6 a = 86

Substitute the given value of a into the equation 1028 s - 6 a = 86

1028 s - 6 \times \frac{1017 s}{2} = 86

Simplify

More Steps

Evaluate

1028 s - 6 \times \frac{1017 s}{2}

Multiply the terms

More Steps

Multiply the terms

6 \times \frac{1017 s}{2}

Cancel out the common factor 2

3 \times 1017 s

Multiply the terms

3051 s

1028 s - 3051 s

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

(1028 - 3051) s

Subtract the numbers

- 2023 s

- 2023 s = 86

Change the signs on both sides of the equation

2023 s = - 86

Divide both sides

\frac{2023 s}{2023} = \frac{- 86}{2023}

Divide the numbers

s = \frac{- 86}{2023}

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

s = - \frac{86}{2023}

Substitute the given value of s into the equation a = \frac{1017 s}{2}

a = \frac{1017 ( - \frac{86}{2023} )}{2}

Calculate

a = - \frac{43731}{2023}

Calculate

{a = - \frac{43731}{2023} s = - \frac{86}{2023}

Check the solution

More Steps

Check the solution

{11 (- \frac{86}{2023}) - 4 (- \frac{43731}{2023}) = 1028 (- \frac{86}{2023}) - 6 (- \frac{43731}{2023}) 1028 (- \frac{86}{2023}) - 6 (- \frac{43731}{2023}) = 86

Simplify

{86 = 86 86 = 86

Evaluate

true

{a = - \frac{43731}{2023} s = - \frac{86}{2023}

Solution

(a, s) = (- \frac{43731}{2023}, - \frac{86}{2023})

Alternative Form

(a, s) \approx (- 21.616906, - 0.042511)

Show Solution

Relationship between lines

Neither parallel nor perpendicular

Evaluate

11 s - 4 a = 1028 s - 6 a, 1028 s - 6 a = 86

Write the equation in slope-intercept form

More Steps

Evaluate

11 s - 4 a = 1028 s - 6 a

Move the expression to the right side

11 s = 1028 s - 2 a

Move the expression to the left side

- 1017 s = - 2 a

Divide both sides

s = \frac{2}{1017} a

s = \frac{2}{1017} a, 1028 s - 6 a = 86

Write the equation in slope-intercept form

More Steps

Evaluate

1028 s - 6 a = 86

Move the expression to the right side

1028 s = 86 + 6 a

Divide both sides

s = \frac{43}{514} + \frac{3}{514} a

Rearrange the terms

s = \frac{3}{514} a + \frac{43}{514}

s = \frac{2}{1017} a, s = \frac{3}{514} a + \frac{43}{514}

Since the line is in slope-intercept form, the coefficient \frac{2}{1017} is the slope of the line

\frac{2}{1017}, s = \frac{3}{514} a + \frac{43}{514}

Since the line is in slope-intercept form, the coefficient \frac{3}{514} is the slope of the line

\frac{2}{1017}, \frac{3}{514}

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

\frac{2}{1017} \times \frac{3}{514}

Reduce the numbers

\frac{1}{1017} \times \frac{3}{257}

Reduce the numbers

\frac{1}{339} \times \frac{1}{257}

To multiply the fractions,multiply the numerators and denominators separately

\frac{1}{339 \times 257}

Multiply the numbers

\frac{1}{87123}

Solution

Neither parallel nor perpendicular

Show Solution