Algebra
Calculus
Trigonometry
Matrix
Question
Solve the system of equations
Solve using the substitution method
Solve using the elimination method
(x1,y1)=(−21,0)(x2,y2)=(51,−57)
Evaluate
{y=5xy5xy=−2x−1
Solve the equation
More Steps
Evaluate
y=5xy
Move the expression to the left side
y−5xy=0
Factor the expression
y(1−5x)=0
Separate the equation into 2 possible cases
y=0∪1−5x=0
Solve the equation
More Steps
Evaluate
1−5x=0
Move the constant to the right-hand side and change its sign
−5x=0−1
Removing 0 doesn't change the value,so remove it from the expression
−5x=−1
Change the signs on both sides of the equation
5x=1
Divide both sides
55x=51
Divide the numbers
x=51
y=0∪x=51
Find the union
x=51∪y=0
{y=0∪x=515xy=−2x−1
Evaluate
{y=05xy=−2x−1∪{x=515xy=−2x−1
Calculate
More Steps
Evaluate
{y=05xy=−2x−1
Substitute the given value of y into the equation 5xy=−2x−1
5x×0=−2x−1
Any expression multiplied by 0 equals 0
0=−2x−1
Swap the sides of the equation
−2x−1=0
Move the constant to the right-hand side and change its sign
−2x=0+1
Removing 0 doesn't change the value,so remove it from the expression
−2x=1
Change the signs on both sides of the equation
2x=−1
Divide both sides
22x=2−1
Divide the numbers
x=2−1
Use b−a=−ba=−ba to rewrite the fraction
x=−21
Calculate
{x=−21y=0
{x=−21y=0∪{x=515xy=−2x−1
Calculate
More Steps
Evaluate
{x=515xy=−2x−1
Substitute the given value of x into the equation 5xy=−2x−1
5×51y=−2×51−1
Simplify
y=−2×51−1
Simplify
More Steps
Evaluate
−2×51−1
Multiply the numbers
−52−1
Reduce fractions to a common denominator
−52−55
Write all numerators above the common denominator
5−2−5
Subtract the numbers
5−7
Use b−a=−ba=−ba to rewrite the fraction
−57
y=−57
Calculate
{x=51y=−57
{x=−21y=0∪{x=51y=−57
Check the solution
More Steps
Check the solution
{0=5(−21)×05(−21)×0=−2(−21)−1
Simplify
{0=00=0
Evaluate
true
{x=−21y=0∪{x=51y=−57
Check the solution
More Steps
Check the solution
{−57=5×51(−57)5×51(−57)=−2×51−1
Simplify
{−1.4=−1.4−1.4=−1.4
Evaluate
true
{x=−21y=0∪{x=51y=−57
Solution
(x1,y1)=(−21,0)(x2,y2)=(51,−57)
Show Solution
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