Algebra
Calculus
Trigonometry
Matrix
Question
Solve the system of equations
Solve using the substitution method
Solve using the elimination method
(x1,y1)=(10×230012−52904600001150+1322615,10−1150+1322615)(x2,y2)=(10×230012−52904600001150−1322615,−101150+1322615)
Evaluate
{x−y=200xy200xy=230
Solve the equation for x
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Evaluate
x−y=200xy
Evaluate
x−y=200yx
Move the variable to the left side
x−y−200yx=0
Collect like terms by calculating the sum or difference of their coefficients
(1−200y)x−y=0
Move the constant to the right side
(1−200y)x=0+y
Removing 0 doesn't change the value,so remove it from the expression
(1−200y)x=y
Divide both sides
1−200y(1−200y)x=1−200yy
Divide the numbers
x=1−200yy
{x=1−200yy200xy=230
Substitute the given value of x into the equation 200xy=230
200×1−200yy×y=230
Simplify
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Evaluate
200×1−200yy×y
Multiply the terms
1−200y200y×y
Multiply the terms
1−200y200y×y
Multiply the terms
1−200y200y2
1−200y200y2=230
Cross multiply
200y2=(1−200y)×230
Simplify the equation
200y2=230(1−200y)
Rewrite the expression
10×20y2=10×23(1−200y)
Evaluate
20y2=23(1−200y)
Expand the expression
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Evaluate
23(1−200y)
Apply the distributive property
23×1−23×200y
Any expression multiplied by 1 remains the same
23−23×200y
Multiply the numbers
23−4600y
20y2=23−4600y
Move the expression to the left side
20y2−(23−4600y)=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
20y2−23+4600y=0
Rewrite in standard form
20y2+4600y−23=0
Substitute a=20,b=4600 and c=−23 into the quadratic formula y=2a−b±b2−4ac
y=2×20−4600±46002−4×20(−23)
Simplify the expression
y=40−4600±46002−4×20(−23)
Simplify the expression
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Evaluate
46002−4×20(−23)
Multiply
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Multiply the terms
4×20(−23)
Rewrite the expression
−4×20×23
Multiply the terms
−1840
46002−(−1840)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
46002+1840
y=40−4600±46002+1840
Simplify the radical expression
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Evaluate
46002+1840
Add the numbers
21161840
Write the expression as a product where the root of one of the factors can be evaluated
16×1322615
Write the number in exponential form with the base of 4
42×1322615
The root of a product is equal to the product of the roots of each factor
42×1322615
Reduce the index of the radical and exponent with 2
41322615
y=40−4600±41322615
Separate the equation into 2 possible cases
y=40−4600+41322615y=40−4600−41322615
Simplify the expression
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Evaluate
y=40−4600+41322615
Divide the terms
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Evaluate
40−4600+41322615
Rewrite the expression
404(−1150+1322615)
Cancel out the common factor 4
10−1150+1322615
y=10−1150+1322615
y=10−1150+1322615y=40−4600−41322615
Simplify the expression
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Evaluate
y=40−4600−41322615
Divide the terms
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Evaluate
40−4600−41322615
Rewrite the expression
404(−1150−1322615)
Cancel out the common factor 4
10−1150−1322615
Use b−a=−ba=−ba to rewrite the fraction
−101150+1322615
y=−101150+1322615
y=10−1150+1322615y=−101150+1322615
Evaluate the logic
y=10−1150+1322615∪y=−101150+1322615
Rearrange the terms
{x=1−200yyy=10−1150+1322615∪{x=1−200yyy=−101150+1322615
Calculate
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Evaluate
{x=1−200yyy=10−1150+1322615
Substitute the given value of y into the equation x=1−200yy
x=1−200×10−1150+132261510−1150+1322615
Calculate
x=10×230012−52904600001150+1322615
Calculate
{x=10×230012−52904600001150+1322615y=10−1150+1322615
{x=10×230012−52904600001150+1322615y=10−1150+1322615∪{x=1−200yyy=−101150+1322615
Calculate
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Evaluate
{x=1−200yyy=−101150+1322615
Substitute the given value of y into the equation x=1−200yy
x=1−200(−101150+1322615)−101150+1322615
Simplify the expression
x=−1−200(−101150+1322615)101150+1322615
Calculate
x=10×230012−52904600001150−1322615
Calculate
{x=10×230012−52904600001150−1322615y=−101150+1322615
{x=10×230012−52904600001150+1322615y=10−1150+1322615∪{x=10×230012−52904600001150−1322615y=−101150+1322615
Check the solution
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Check the solution
{10×230012−52904600001150+1322615−10−1150+1322615=200×10×230012−52904600001150+1322615×10−1150+1322615200×10×230012−52904600001150+1322615×10−1150+1322615=230
Simplify
{230=230230=230
Evaluate
true
{x=10×230012−52904600001150+1322615y=10−1150+1322615∪{x=10×230012−52904600001150−1322615y=−101150+1322615
Check the solution
More Steps
Check the solution
⎩⎨⎧10×230012−52904600001150−1322615−(−101150+1322615)=200×10×230012−52904600001150−1322615×(−101150+1322615)200×10×230012−52904600001150−1322615×(−101150+1322615)=230
Simplify
{230=230230=230
Evaluate
true
{x=10×230012−52904600001150+1322615y=10−1150+1322615∪{x=10×230012−52904600001150−1322615y=−101150+1322615
Solution
(x1,y1)=(10×230012−52904600001150+1322615,10−1150+1322615)(x2,y2)=(10×230012−52904600001150−1322615,−101150+1322615)
Show Solution
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