Question
Solve the system of equations
(x1,y1)=(61+37,61−37)(x2,y2)=(61−37,61+37)
Evaluate
{xy=0−3x−3y0−3x−3y=−1
Removing 0 doesn't change the value,so remove it from the expression
{xy=−3x−3y0−3x−3y=−1
Removing 0 doesn't change the value,so remove it from the expression
{xy=−3x−3y−3x−3y=−1
Solve the equation for x
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Evaluate
−3x−3y=−1
Move the expression to the right-hand side and change its sign
−3x=−1+3y
Change the signs on both sides of the equation
3x=1−3y
Divide both sides
33x=31−3y
Divide the numbers
x=31−3y
{xy=−3x−3yx=31−3y
Substitute the given value of x into the equation xy=−3x−3y
31−3y×y=−3×31−3y−3y
Simplify
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Evaluate
31−3y×y
Multiply the terms
3(1−3y)y
Multiply the terms
3y(1−3y)
3y(1−3y)=−3×31−3y−3y
Simplify
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Evaluate
−3×31−3y−3y
Multiply the terms
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Multiply the terms
−3×31−3y
Cancel out the common factor 3
−1×(1−3y)
Multiply the terms
−(1−3y)
Calculate
−1+3y
−1+3y−3y
The sum of two opposites equals 0
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Evaluate
3y−3y
Collect like terms
(3−3)y
Add the coefficients
0×y
Calculate
0
−1+0
Remove 0
−1
3y(1−3y)=−1
Cross multiply
y(1−3y)=3(−1)
Simplify the equation
y(1−3y)=−3
Expand the expression
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Evaluate
y(1−3y)
Apply the distributive property
y×1−y×3y
Any expression multiplied by 1 remains the same
y−y×3y
Multiply the terms
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Evaluate
y×3y
Use the commutative property to reorder the terms
3y×y
Multiply the terms
3y2
y−3y2
y−3y2=−3
Move the expression to the left side
y−3y2−(−3)=0
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
y−3y2+3=0
Rewrite in standard form
−3y2+y+3=0
Multiply both sides
3y2−y−3=0
Substitute a=3,b=−1 and c=−3 into the quadratic formula y=2a−b±b2−4ac
y=2×31±(−1)2−4×3(−3)
Simplify the expression
y=61±(−1)2−4×3(−3)
Simplify the expression
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Evaluate
(−1)2−4×3(−3)
Evaluate the power
1−4×3(−3)
Multiply
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Multiply the terms
4×3(−3)
Rewrite the expression
−4×3×3
Multiply the terms
−36
1−(−36)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
1+36
Add the numbers
37
y=61±37
Separate the equation into 2 possible cases
y=61+37y=61−37
Evaluate the logic
y=61+37∪y=61−37
Rearrange the terms
{x=31−3yy=61+37∪{x=31−3yy=61−37
Calculate
More Steps

Evaluate
{x=31−3yy=61+37
Substitute the given value of y into the equation x=31−3y
x=31−3×61+37
Calculate
x=61−37
Calculate
{x=61−37y=61+37
{x=61−37y=61+37∪{x=31−3yy=61−37
Calculate
More Steps

Evaluate
{x=31−3yy=61−37
Substitute the given value of y into the equation x=31−3y
x=31−3×61−37
Calculate
x=61+37
Calculate
{x=61+37y=61−37
{x=61−37y=61+37∪{x=61+37y=61−37
Calculate
{x=61+37y=61−37∪{x=61−37y=61+37
Check the solution
More Steps

Check the solution
{61+37×61−37=0−3×61+37−3×61−370−3×61+37−3×61−37=−1
Simplify
{−1=−1−1=−1
Evaluate
true
{x=61+37y=61−37∪{x=61−37y=61+37
Check the solution
More Steps

Check the solution
{61−37×61+37=0−3×61−37−3×61+370−3×61−37−3×61+37=−1
Simplify
{−1=−1−1=−1
Evaluate
true
{x=61+37y=61−37∪{x=61−37y=61+37
Solution
(x1,y1)=(61+37,61−37)(x2,y2)=(61−37,61+37)
Show Solution
