Algebra
Calculus
Trigonometry
Matrix
Question
Solve the system of equations
Solve using the substitution method
Solve using the elimination method
(x1,y1)=(−5776+4418,19−38+2418)(x2,y2)=(574418−76,−1938+2418)
Evaluate
{−3x−2y=−19xy−19xy=8
Solve the equation for x
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Evaluate
−3x−2y=−19xy
Evaluate
−3x−2y=−19yx
Move the variable to the left side
−3x−2y+19yx=0
Collect like terms by calculating the sum or difference of their coefficients
(−3+19y)x−2y=0
Move the constant to the right side
(−3+19y)x=0+2y
Removing 0 doesn't change the value,so remove it from the expression
(−3+19y)x=2y
Divide both sides
−3+19y(−3+19y)x=−3+19y2y
Divide the numbers
x=−3+19y2y
{x=−3+19y2y−19xy=8
Substitute the given value of x into the equation −19xy=8
−19×−3+19y2y×y=8
Multiply the terms
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Evaluate
−19×−3+19y2y×y
Multiply the terms
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Evaluate
19×−3+19y2y×y
Multiply the terms
−3+19y38y×y
Multiply the terms
−3+19y38y×y
Multiply the terms
−3+19y38y2
−−3+19y38y2
−−3+19y38y2=8
Rewrite the expression
−3+19y−38y2=8
Cross multiply
−38y2=(−3+19y)×8
Simplify the equation
−38y2=8(−3+19y)
Rewrite the expression
2(−19y2)=2×4(−3+19y)
Evaluate
−19y2=4(−3+19y)
Expand the expression
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Evaluate
4(−3+19y)
Apply the distributive property
4(−3)+4×19y
Multiply the numbers
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Evaluate
4(−3)
Multiplying or dividing an odd number of negative terms equals a negative
−4×3
Multiply the numbers
−12
−12+4×19y
Multiply the numbers
−12+76y
−19y2=−12+76y
Move the expression to the left side
−19y2−(−12+76y)=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
−19y2+12−76y=0
Rewrite in standard form
−19y2−76y+12=0
Multiply both sides
19y2+76y−12=0
Substitute a=19,b=76 and c=−12 into the quadratic formula y=2a−b±b2−4ac
y=2×19−76±762−4×19(−12)
Simplify the expression
y=38−76±762−4×19(−12)
Simplify the expression
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Evaluate
762−4×19(−12)
Multiply
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Multiply the terms
4×19(−12)
Rewrite the expression
−4×19×12
Multiply the terms
−912
762−(−912)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
762+912
Evaluate the power
5776+912
Add the numbers
6688
y=38−76±6688
Simplify the radical expression
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Evaluate
6688
Write the expression as a product where the root of one of the factors can be evaluated
16×418
Write the number in exponential form with the base of 4
42×418
The root of a product is equal to the product of the roots of each factor
42×418
Reduce the index of the radical and exponent with 2
4418
y=38−76±4418
Separate the equation into 2 possible cases
y=38−76+4418y=38−76−4418
Simplify the expression
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Evaluate
y=38−76+4418
Divide the terms
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Evaluate
38−76+4418
Rewrite the expression
382(−38+2418)
Cancel out the common factor 2
19−38+2418
y=19−38+2418
y=19−38+2418y=38−76−4418
Simplify the expression
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Evaluate
y=38−76−4418
Divide the terms
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Evaluate
38−76−4418
Rewrite the expression
382(−38−2418)
Cancel out the common factor 2
19−38−2418
Use b−a=−ba=−ba to rewrite the fraction
−1938+2418
y=−1938+2418
y=19−38+2418y=−1938+2418
Evaluate the logic
y=19−38+2418∪y=−1938+2418
Rearrange the terms
{x=−3+19y2yy=19−38+2418∪{x=−3+19y2yy=−1938+2418
Calculate
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Evaluate
{x=−3+19y2yy=19−38+2418
Substitute the given value of y into the equation x=−3+19y2y
x=−3+19×19−38+24182×19−38+2418
Calculate
x=−5776+4418
Calculate
{x=−5776+4418y=19−38+2418
{x=−5776+4418y=19−38+2418∪{x=−3+19y2yy=−1938+2418
Calculate
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Evaluate
{x=−3+19y2yy=−1938+2418
Substitute the given value of y into the equation x=−3+19y2y
x=−3+19(−1938+2418)2(−1938+2418)
Calculate
x=574418−76
Calculate
{x=574418−76y=−1938+2418
{x=−5776+4418y=19−38+2418∪{x=574418−76y=−1938+2418
Check the solution
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Check the solution
⎩⎨⎧−3(−5776+4418)−2×19−38+2418=−19(−5776+4418)×19−38+2418−19(−5776+4418)×19−38+2418=8
Simplify
{8=88=8
Evaluate
true
{x=−5776+4418y=19−38+2418∪{x=574418−76y=−1938+2418
Check the solution
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Check the solution
⎩⎨⎧−3×574418−76−2(−1938+2418)=−19×574418−76×(−1938+2418)−19×574418−76×(−1938+2418)=8
Simplify
{8=88=8
Evaluate
true
{x=−5776+4418y=19−38+2418∪{x=574418−76y=−1938+2418
Solution
(x1,y1)=(−5776+4418,19−38+2418)(x2,y2)=(574418−76,−1938+2418)
Show Solution
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