Algebra
Calculus
Trigonometry
Matrix
Question
Solve the system of equations
(x1,y1)=(141+15,2−1+15)(x2,y2)=(141−15,−21+15)
Evaluate
{2xy=7x−y7x−y=1
Solve the equation for y
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Evaluate
7x−y=1
Move the expression to the right-hand side and change its sign
−y=1−7x
Change the signs on both sides of the equation
y=−1+7x
{2xy=7x−yy=−1+7x
Substitute the given value of y into the equation 2xy=7x−y
2x(−1+7x)=7x−(−1+7x)
Simplify
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Evaluate
7x−(−1+7x)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
7x+1−7x
The sum of two opposites equals 0
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Evaluate
7x−7x
Collect like terms
(7−7)x
Add the coefficients
0×x
Calculate
0
0+1
Remove 0
1
2x(−1+7x)=1
Expand the expression
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Evaluate
2x(−1+7x)
Apply the distributive property
2x(−1)+2x×7x
Multiply the numbers
−2x+2x×7x
Multiply the terms
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Evaluate
2x×7x
Multiply the numbers
14x×x
Multiply the terms
14x2
−2x+14x2
−2x+14x2=1
Move the expression to the left side
−2x+14x2−1=0
Rewrite in standard form
14x2−2x−1=0
Substitute a=14,b=−2 and c=−1 into the quadratic formula x=2a−b±b2−4ac
x=2×142±(−2)2−4×14(−1)
Simplify the expression
x=282±(−2)2−4×14(−1)
Simplify the expression
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Evaluate
(−2)2−4×14(−1)
Multiply
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Multiply the terms
4×14(−1)
Any expression multiplied by 1 remains the same
−4×14
Multiply the terms
−56
(−2)2−(−56)
Rewrite the expression
22−(−56)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
22+56
Evaluate the power
4+56
Add the numbers
60
x=282±60
Simplify the radical expression
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Evaluate
60
Write the expression as a product where the root of one of the factors can be evaluated
4×15
Write the number in exponential form with the base of 2
22×15
The root of a product is equal to the product of the roots of each factor
22×15
Reduce the index of the radical and exponent with 2
215
x=282±215
Separate the equation into 2 possible cases
x=282+215x=282−215
Simplify the expression
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Evaluate
x=282+215
Divide the terms
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Evaluate
282+215
Rewrite the expression
282(1+15)
Cancel out the common factor 2
141+15
x=141+15
x=141+15x=282−215
Simplify the expression
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Evaluate
x=282−215
Divide the terms
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Evaluate
282−215
Rewrite the expression
282(1−15)
Cancel out the common factor 2
141−15
x=141−15
x=141+15x=141−15
Evaluate the logic
x=141+15∪x=141−15
Rearrange the terms
{x=141+15y=−1+7x∪{x=141−15y=−1+7x
Calculate
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Evaluate
{x=141+15y=−1+7x
Substitute the given value of x into the equation y=−1+7x
y=−1+7×141+15
Calculate
y=2−1+15
Calculate
{x=141+15y=2−1+15
{x=141+15y=2−1+15∪{x=141−15y=−1+7x
Calculate
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Evaluate
{x=141−15y=−1+7x
Substitute the given value of x into the equation y=−1+7x
y=−1+7×141−15
Calculate
y=−21+15
Calculate
{x=141−15y=−21+15
{x=141+15y=2−1+15∪{x=141−15y=−21+15
Check the solution
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Check the solution
{2×141+15×2−1+15=7×141+15−2−1+157×141+15−2−1+15=1
Simplify
{1=11=1
Evaluate
true
{x=141+15y=2−1+15∪{x=141−15y=−21+15
Check the solution
More Steps
Check the solution
⎩⎨⎧2×141−15×(−21+15)=7×141−15−(−21+15)7×141−15−(−21+15)=1
Simplify
{1=11=1
Evaluate
true
{x=141+15y=2−1+15∪{x=141−15y=−21+15
Solution
(x1,y1)=(141+15,2−1+15)(x2,y2)=(141−15,−21+15)
Show Solution
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