Math Please Help?

Question

Here is the questions:

Condisder the following system of two equations with two unknowns x and y. Assume that A1,A2 and B1,B2 are know.

Y = A1(X) + B1
Y = A2(X) + B2

ASSUMING THAT A1 DOSE NOT EQUAL A2, SOLVE FOR X AND Y.

Thanks. It's been a while since Algebra I just need someone to show the work to relearn how to do more of these problems.

Answer 1

since you got two equations subtract it
(Y = A1(X) + B1) - (Y = A2(X) + B2)
results in

0 = (A1-A2)X + (B1-B2)
-(B1-B2) = (A1-A2)X
-(B1-B2) / (A1-A2) = x
now you know x you can solve for y

Answer 2

Just set the two equations equal to one another:

a1(x) + b1 = a2(x) + b2

and solve for x

(a1 - a2)x = (b2 - b1)

x = (b2-b1) / (a1 - a2)

So, y = a1(b2-b1)/(a1-a2) + b1

Answer 3

Multiply top by A2 and bottom by A1

A2*Y = A1*A2*x + A2*B1
A1*Y = A2*A1*x + A1*B2

Subtract bottom equation from top equation

(A2 - A1)Y = A2*B1 - A1*B2

Y = (A2*B1 - A1*B2)/(A2 - A1)

To get X substitute Y into one of the equations and solve for X.

Bozo

Answer 4

Y = A1(X) + B1
Y = A2(X) + B2

subtract the two equations:

(Y - Y) = (A1*x - A2 * x) + (B1 - B2)
0 = (A1*x - A2 * x) + (B1 - B2)
(B2 - B1) = (A1*x - A2 * x)
(B2 - B1) = (A1 - A2)*x
(B2 - B1) / (A1 - A2) = x

now plug in

Y = A1(X) + B1
Y = A1((B2 - B1) / (A1 - A2)) + B1


-OR-

Y = A1(X) + B1
Y = A2(X) + B2

set them equal,

A1(X) + B1 = A2(X) + B2

(and go from there)

-OR-

rewrite them like this:

Y - A1(X) = B1
Y - A2(X) = B2

Now you have a matrix,

(1 -A1) (Y) = (B1)
(1 -A2) (X) = (B2)

Shorthand,

(1 -A1 | B1)
(1 -A2 | B2)

And let the TI-(whatever) solve it

Answer 5

Subtract the first equation from the second

y-y=
(A2-A1)(X)+B2-B1

(B1-B2)/(A2-A1)=x

y=A1*(B1-B2)/(A2-A1)+B1
or
y=A2*(B1-B2)/(A2-A1)+B2

j