3x + 14y = 5xy
21y - x = 2xy
kindly solve the pair of linear equation
1.Divide the two equations by xy
2.You will now have two equations.
3.Solve it by multiplying and cancelling , and find x and y by substituting.
To solve the pair of linear equations, we can use the method of substitution or elimination. Let's use the method of substitution:
Step 1: Solve one equation for one variable in terms of the other variable.
Let's solve the second equation for x:
21y - x = 2xy
Re-arranging the equation:
x = 21y - 2xy
Step 2: Substitute this expression for x into the other equation.
3x + 14y = 5xy
Substituting the value of x into the equation:
3(21y - 2xy) + 14y = 5xy
Now we can solve this equation for y:
Step 3: Simplify and solve for y
Multiplying through:
63y - 6xy + 14y = 5xy
Adding like terms:
77y - 6xy = 5xy
Step 4: Move all the terms involving y on one side and those involving x on the other side:
77y = 11xy + 6xy
77y = 17xy
Now, we can solve for y:
y = 0 (by dividing both sides by 77)
Step 5: Substitute the value of y back into one of the equations to solve for x.
Using the first equation:
3x + 14(0) = 5x(0)
3x = 0
Hence, the solution to the pair of linear equations is x = 0 and y = 0.
Not got it 🤔😒
I don't now
note from #2 that
x = 21y/(2y+1)
put that into #1 and you have
3*21y/(2y+1) + 14y = 5y*21y/(2y+1)
63y + 14y(2y+1) = 105y^2
77y^2-77y = 0
77y(y-1) = 0
Now you have two solutions for y. Use them to get associated solutions for x.