Answer:
105 mph = rate of first plane
130 mph = rate of second plane
Step-by-step explanation:
Let r = rate of first plane
then r + 25 = rate of second plane
2r = distance of first plane
2(r + 25) = distance of second plane
2r + 2(r + 25) = 470
2r + 2r + 50 = 470
4r = 420
r = 105 mph
r + 25 = 130 mph
Answer:
x=2, x=1
Step-by-step explanation:
Multiply both sides by x, so you get (x^2)+2=3x, which comes from 
Solve for (x^2)+2=3x
(x^2)-3x+2=0
(x-2)(x-1)=0, use box method or FOIL if needed
x=2,x=1
x=31,y=−61
Put the equations in standard form and then use matrices to solve the system of equations.
5x+4y=1,3x−6y=2
Write the equations in matrix form.
(534−6)(xy)=(12)
Left multiply the equation by the inverse matrix of (534−6).
inverse((534−6))(534−6)(xy)=inverse((534−6))(12)
The product of a matrix and its inverse is the identity matrix.
(1001)(xy)=inverse((534−6))(12)
Multiply the matrices on the left hand side of the equal sign.
(xy)=inverse((534−6))(12)
For the 2×2 matrix (acbd), the inverse matrix is (ad−bcdad−bc−cad−bc−bad−bca), so the matrix equation can be rewritten as a matrix multiplication problem.
(xy)=(5(−6)−4×3−6−5(−6)−4×33−5(−6)−4×345(−6)−4×35)(12)
Do the arithmetic.
(xy)=(71141212−425)(12)
Multiply the matrices.
(xy)=(71+212×2141−425×2)
Do the arithmetic.
(xy)=(31−61)
Extract the matrix elements x and y.
x=31,y=−61
