Algebra
Calculus
Trigonometry
Matrix
Question
Solve the system of equations
(x1,y1)=(−0.545184,3.364448)(x2,y2)=(−1.52295,0.43115)(x3,y3)=(0.401467,6.204402)
Evaluate
{5x2y=1×y−3x3y1×y−3x3y=5
Any expression multiplied by 1 remains the same
{5x2y=y−3x3y1×y−3x3y=5
Any expression multiplied by 1 remains the same
{5x2y=y−3x3yy−3x3y=5
Solve the equation
More Steps
Evaluate
5x2y=y−3x3y
Move the expression to the left side
5x2y−(y−3x3y)=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
5x2y−y+3x3y=0
Factor the expression
y(5x2−1+3x3)=0
Separate the equation into 2 possible cases
y=0∪5x2−1+3x3=0
Solve the equation
y=0∪x≈−1.52295∪x≈−0.545184∪x≈0.401467
Find the union
x≈−1.52295∪x≈−0.545184∪x≈0.401467∪y=0
{y=0∪x≈−1.52295∪x≈−0.545184∪x≈0.401467y−3x3y=5
Evaluate
{y=0y−3x3y=5∪{x≈−1.52295y−3x3y=5∪{x≈−0.545184y−3x3y=5∪{x≈0.401467y−3x3y=5
Calculate
More Steps
Evaluate
{y=0y−3x3y=5
Substitute the given value of y into the equation y−3x3y=5
0−3x3×0=5
Simplify
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Evaluate
0−3x3×0
Any expression multiplied by 0 equals 0
0−0
Subtract the terms
0
0=5
Calculate
{x∈∅y∈∅
{x∈∅y∈∅∪{x≈−1.52295y−3x3y=5∪{x≈−0.545184y−3x3y=5∪{x≈0.401467y−3x3y=5
Calculate
More Steps
Evaluate
{x≈−1.52295y−3x3y=5
Substitute the given value of x into the equation y−3x3y=5
y−3(−1.52295)3y=5
Simplify
More Steps
Evaluate
y−3(−1.52295)3y
Multiply the terms
y−(−10.596882y)
Rewrite the expression
y+10.596882y
Collect like terms by calculating the sum or difference of their coefficients
(1+10.596882)y
Add the numbers
11.596882y
11.596882y=5
Divide both sides
11.59688211.596882y=11.5968825
Divide the numbers
y=11.5968825
Divide the numbers
y≈0.43115
Calculate
{x≈−1.52295y≈0.43115
{x∈∅y∈∅∪{x≈−1.52295y≈0.43115∪{x≈−0.545184y−3x3y=5∪{x≈0.401467y−3x3y=5
Calculate
More Steps
Evaluate
{x≈−0.545184y−3x3y=5
Substitute the given value of x into the equation y−3x3y=5
y−3(−0.545184)3y=5
Simplify
More Steps
Evaluate
y−3(−0.545184)3y
Multiply the terms
y−(−0.486128y)
Rewrite the expression
y+0.486128y
Collect like terms by calculating the sum or difference of their coefficients
(1+0.486128)y
Add the numbers
1.486128y
1.486128y=5
Divide both sides
1.4861281.486128y=1.4861285
Divide the numbers
y=1.4861285
Divide the numbers
y≈3.364448
Calculate
{x≈−0.545184y≈3.364448
{x∈∅y∈∅∪{x≈−1.52295y≈0.43115∪{x≈−0.545184y≈3.364448∪{x≈0.401467y−3x3y=5
Calculate
More Steps
Evaluate
{x≈0.401467y−3x3y=5
Substitute the given value of x into the equation y−3x3y=5
y−3×0.4014673y=5
Simplify
More Steps
Evaluate
y−3×0.4014673y
Multiply the terms
y−0.194121y
Collect like terms by calculating the sum or difference of their coefficients
(1−0.194121)y
Subtract the numbers
0.805879y
0.805879y=5
Divide both sides
0.8058790.805879y=0.8058795
Divide the numbers
y=0.8058795
Divide the numbers
y≈6.204402
Calculate
{x≈0.401467y≈6.204402
{x∈∅y∈∅∪{x≈−1.52295y≈0.43115∪{x≈−0.545184y≈3.364448∪{x≈0.401467y≈6.204402
Rearrange the terms
{x≈−0.545184y≈3.364448∪{x≈−1.52295y≈0.43115∪{x≈0.401467y≈6.204402
Check the solution
{x≈−0.545184y≈3.364448∪{x≈−1.52295y≈0.43115∪{x≈0.401467y≈6.204402
Solution
(x1,y1)=(−0.545184,3.364448)(x2,y2)=(−1.52295,0.43115)(x3,y3)=(0.401467,6.204402)
Show Solution
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