Algebra
Calculus
Trigonometry
Matrix
Question
Solve the system of equations
Solve using the substitution method
Solve using the elimination method
Solve using the Gauss-Jordan method
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(x,y)=(−41,−21)
Alternative Form
(x,y)=(−0.25,−0.5)
Evaluate
{2x+y=8x−2y8x−2y=−1
Solve the equation for x
More Steps
Evaluate
2x+y=8x−2y
Move the expression to the left side
2x+y−8x=−2y
Move the expression to the right side
2x−8x=−2y−y
Add and subtract
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Evaluate
2x−8x
Collect like terms by calculating the sum or difference of their coefficients
(2−8)x
Subtract the numbers
−6x
−6x=−2y−y
Add and subtract
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Evaluate
−2y−y
Collect like terms by calculating the sum or difference of their coefficients
(−2−1)y
Subtract the numbers
−3y
−6x=−3y
Change the signs on both sides of the equation
6x=3y
Divide both sides
66x=63y
Divide the numbers
x=63y
Cancel out the common factor 3
x=2y
{x=2y8x−2y=−1
Substitute the given value of x into the equation 8x−2y=−1
8×2y−2y=−1
Simplify
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Evaluate
8×2y−2y
Cancel out the common factor 2
4y−2y
Collect like terms by calculating the sum or difference of their coefficients
(4−2)y
Subtract the numbers
2y
2y=−1
Divide both sides
22y=2−1
Divide the numbers
y=2−1
Use b−a=−ba=−ba to rewrite the fraction
y=−21
Substitute the given value of y into the equation x=2y
x=2−21
Simplify the expression
x=−221
Calculate
x=−41
Calculate
{x=−41y=−21
Check the solution
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Check the solution
{2(−41)−21=8(−41)−2(−21)8(−41)−2(−21)=−1
Simplify
{−1=−1−1=−1
Evaluate
true
{x=−41y=−21
Solution
(x,y)=(−41,−21)
Alternative Form
(x,y)=(−0.25,−0.5)
Show Solution
Relationship between lines
Neither parallel nor perpendicular
Evaluate
2x+y=8x−2y,8x−2y=−1
Write the equation in slope-intercept form
More Steps
Evaluate
2x+y=8x−2y
Move the expression to the right side
y=6x−2y
Move the expression to the left side
3y=6x
Divide both sides
y=2x
y=2x,8x−2y=−1
Write the equation in slope-intercept form
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Evaluate
8x−2y=−1
Move the expression to the right side
−2y=−1−8x
Divide both sides
y=21+4x
Rearrange the terms
y=4x+21
y=2x,y=4x+21
Since the line is in slope-intercept form, the coefficient 2 is the slope of the line
2,y=4x+21
Since the line is in slope-intercept form, the coefficient 4 is the slope of the line
2,4
The slopes are different, so the lines aren't parallel. We'll multiply the slopes to check their relationship
2×4
Multiply the numbers
8
Solution
Neither parallel nor perpendicular
Show Solution
Graph
