SOLUTION: write the equations for 2 lines that intersect at the point (1,0). explain how you know the answer is correct.

the equations for 2 lines that intersect at the point (1,0). 



Equations of any line can all be written Ax + By = C



Since you know it goes through the point (1, 0), replace x by 1 and y by 0:



A(1) + B(0) = C

A = C



Now choose any number in the world at random for A and C to equal, and any

number in the world at random for B.  I will arbitrarily choose 3 for both

A and C and -2 for B.  So Ax + By = C becomes



3x - 2y = 3



Now do it again, but don't make the same choices as before.  This time, I

will arbitrarily choose 4 for both A and C and 7 for B. So Ax + By = C

becomes



4x + 7y = 4



explain how you know the answer is correct.



I will check the system 



3x - 2y = 3

4x + 7y = 4



to see if (x, y) = (1, 0) is the solution:



3(1) - 2(0) = 3

4(1) + 7(0) = 4



So I get 3 = 3 in the first and 4 = 4 in the second, so it is correct.



Edwin

AnlytcPhil@aol.com