Algebra
Calculus
Trigonometry
Matrix
Question
Solve the system of equations
(x1,y1)=(−23+13,−55+1513)(x2,y2)=(213−3,−55−1513)
Evaluate
{x2y=1×y−3xy1×y−3xy=−10
Any expression multiplied by 1 remains the same
{x2y=y−3xy1×y−3xy=−10
Any expression multiplied by 1 remains the same
{x2y=y−3xyy−3xy=−10
Solve the equation for x
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Evaluate
y−3xy=−10
Evaluate
y−3yx=−10
Move the expression to the right-hand side and change its sign
−3yx=−10−y
Divide both sides
−3y−3yx=−3y−10−y
Divide the numbers
x=−3y−10−y
Divide the numbers
x=3y10+y
{x2y=y−3xyx=3y10+y
Substitute the given value of x into the equation x2y=y−3xy
(3y10+y)2y=y−3×3y10+y×y
Simplify
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Evaluate
(3y10+y)2y
Rewrite the expression
9y2(10+y)2×y
Reduce the fraction
9y(10+y)2×1
Any expression multiplied by 1 remains the same
9y100+20y+y2
9y100+20y+y2=y−3×3y10+y×y
Simplify
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Evaluate
y−3×3y10+y×y
Multiply the terms
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Multiply the terms
3×3y10+y×y
Multiply the terms
y10+y×y
Cancel out the common factor y
(10+y)×1
Multiply the terms
10+y
y−(10+y)
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−10−y
The sum of two opposites equals 0
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Evaluate
y−y
Collect like terms
(1−1)y
Add the coefficients
0×y
Calculate
0
0−10
Remove 0
−10
9y100+20y+y2=−10
Cross multiply
100+20y+y2=9y(−10)
Simplify the equation
100+20y+y2=−90y
Move the expression to the left side
100+20y+y2−(−90y)=0
Calculate the sum or difference
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Evaluate
100+20y+y2−(−90y)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
100+20y+y2+90y
Add the terms
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Evaluate
20y+90y
Collect like terms by calculating the sum or difference of their coefficients
(20+90)y
Add the numbers
110y
100+110y+y2
100+110y+y2=0
Rewrite in standard form
y2+110y+100=0
Substitute a=1,b=110 and c=100 into the quadratic formula y=2a−b±b2−4ac
y=2−110±1102−4×100
Simplify the expression
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Evaluate
1102−4×100
Multiply the numbers
1102−400
Evaluate the power
12100−400
Subtract the numbers
11700
y=2−110±11700
Simplify the radical expression
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Evaluate
11700
Write the expression as a product where the root of one of the factors can be evaluated
900×13
Write the number in exponential form with the base of 30
302×13
The root of a product is equal to the product of the roots of each factor
302×13
Reduce the index of the radical and exponent with 2
3013
y=2−110±3013
Separate the equation into 2 possible cases
y=2−110+3013y=2−110−3013
Simplify the expression
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Evaluate
y=2−110+3013
Divide the terms
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Evaluate
2−110+3013
Rewrite the expression
22(−55+1513)
Reduce the fraction
−55+1513
y=−55+1513
y=−55+1513y=2−110−3013
Simplify the expression
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Evaluate
y=2−110−3013
Divide the terms
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Evaluate
2−110−3013
Rewrite the expression
22(−55−1513)
Reduce the fraction
−55−1513
y=−55−1513
y=−55+1513y=−55−1513
Evaluate the logic
y=−55+1513∪y=−55−1513
Rearrange the terms
{x=3y10+yy=−55+1513∪{x=3y10+yy=−55−1513
Calculate
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Evaluate
{x=3y10+yy=−55+1513
Substitute the given value of y into the equation x=3y10+y
x=3(−55+1513)10−55+1513
Calculate
x=−23+13
Calculate
{x=−23+13y=−55+1513
{x=−23+13y=−55+1513∪{x=3y10+yy=−55−1513
Calculate
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Evaluate
{x=3y10+yy=−55−1513
Substitute the given value of y into the equation x=3y10+y
x=3(−55−1513)10−55−1513
Calculate
x=213−3
Calculate
{x=213−3y=−55−1513
{x=−23+13y=−55+1513∪{x=213−3y=−55−1513
Check the solution
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Check the solution
⎩⎨⎧(−23+13)2(−55+1513)=1×(−55+1513)−3(−23+13)(−55+1513)1×(−55+1513)−3(−23+13)(−55+1513)=−10
Simplify
{−10=−10−10=−10
Evaluate
true
{x=−23+13y=−55+1513∪{x=213−3y=−55−1513
Check the solution
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Check the solution
⎩⎨⎧(213−3)2(−55−1513)=1×(−55−1513)−3×213−3×(−55−1513)1×(−55−1513)−3×213−3×(−55−1513)=−10
Simplify
{−10=−10−10=−10
Evaluate
true
{x=−23+13y=−55+1513∪{x=213−3y=−55−1513
Solution
(x1,y1)=(−23+13,−55+1513)(x2,y2)=(213−3,−55−1513)
Show Solution
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