Question

If the following system of equations was written as a matrix equation in the form AX = C,?
and matrix A was expressed in the form,

a=[a c]
[b d]

find the value of a - b + c + d.

5x+7y=7
3x-2y=9

Answer 1

So we have...
5 * x + 7 * y = 7
3 * x + (-2)*y = 9

We want to write it in a form like this:
AX = C

[ a c ]
[ b d ] X = C

By comparison, C should be the column vector of our constants on the right-hand side. X should be a column vector of our variables because multiplication of a 2x2 and 2x1 matrix results in a 2x1 matrix. A, then, will be the coefficients of the variables because of how they multiply together.

[a c] [ x ] [7]
[b d] [ y ] = [9]
This left-side multiplies together like this:
[ a(x) + c(y) ] [7 ]
[ b(x) + d(y) ] = [ 9]

This looks more like the original equations now.
ax + cy = 7, bx + dy = 9
5x + 7y = 7 3x - 2y = 9
Can you see these comparisons?
Matrix multiplication is the key piece of information here.

Answer 2

Wait I got lost when you said they multiply together

Answer 3

I say, "they multiply together," referring to the matrices A and X. Is that more clear?

Answer 4

mmm ok , so what would the answer be

Answer 5

this is what it looks like exactly

Answer 6

ax + cy = 7, bx + dy = 9
5x + 7y = 7 3x - 2y = 9
These are the same statements. Comparing those coefficients:
a=5,
c=7
b=3
d=-2
These would be then used.

Answer 7

oooooh ok !!
I get it now:) thank you so much

Answer 8

You're welcome! :)

Answer 9

i'd give you more medals if I could!

Answer 10

wait because its asking for the value of all of those, do I add them all up and whatever I get should be the answer right