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)=(51,−51)
Alternative Form
(x,y)=(0.2,−0.2)
Evaluate
{2x−3y=3x−2y3x−2y=1
Solve the equation for x
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Evaluate
2x−3y=3x−2y
Move the expression to the left side
2x−3y−3x=−2y
Move the expression to the right side
2x−3x=−2y+3y
Add and subtract
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Evaluate
2x−3x
Collect like terms by calculating the sum or difference of their coefficients
(2−3)x
Subtract the numbers
−x
−x=−2y+3y
Add and subtract
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Evaluate
−2y+3y
Collect like terms by calculating the sum or difference of their coefficients
(−2+3)y
Add the numbers
y
−x=y
Change the signs on both sides of the equation
x=−y
{x=−y3x−2y=1
Substitute the given value of x into the equation 3x−2y=1
3(−y)−2y=1
Simplify
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Evaluate
3(−y)−2y
Multiply the numbers
−3y−2y
Collect like terms by calculating the sum or difference of their coefficients
(−3−2)y
Subtract the numbers
−5y
−5y=1
Change the signs on both sides of the equation
5y=−1
Divide both sides
55y=5−1
Divide the numbers
y=5−1
Use b−a=−ba=−ba to rewrite the fraction
y=−51
Substitute the given value of y into the equation x=−y
x=−(−51)
Simplify the expression
x=−(−5)−1
Calculate
x=51
Calculate
{x=51y=−51
Check the solution
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Check the solution
{2×51−3(−51)=3×51−2(−51)3×51−2(−51)=1
Simplify
{1=11=1
Evaluate
true
{x=51y=−51
Solution
(x,y)=(51,−51)
Alternative Form
(x,y)=(0.2,−0.2)
Show Solution
Relationship between lines
Determine whether lines are parallel, perpendicular, or neither
Neither parallel nor perpendicular
Evaluate
2x−3y=3x−2y,3x−2y=1
Write the equation in slope-intercept form
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Evaluate
2x−3y=3x−2y
Move the expression to the right side
−3y=x−2y
Move the expression to the left side
−y=x
Divide both sides
y=−x
y=−x,3x−2y=1
Write the equation in slope-intercept form
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Evaluate
3x−2y=1
Move the expression to the right side
−2y=1−3x
Divide both sides
y=−21+23x
Rearrange the terms
y=23x−21
y=−x,y=23x−21
Since the line is in slope-intercept form, the coefficient −1 is the slope of the line
−1,y=23x−21
Since the line is in slope-intercept form, the coefficient 23 is the slope of the line
−1,23
The slopes are different, so the lines aren't parallel. We'll multiply the slopes to check their relationship
−23
Solution
Neither parallel nor perpendicular
Show Solution