let line A be the graph of the equation x+7y = 3 and let line B be given by the equation 2x + 15y = 6. Use an augmented matrix to determine if the two lines meet and if so at which point. Graph the two lines and indicate their meeting point if it exists.
x+7y=3
7y=-x+3
y= -x/7 + 3/7
slope -1/7
y-intercept 3/7
2x+15y=6
15y=-2x+6
slope -2/15
y-intercept 2/5
I don't have a meeting point. Is this correct?
so far, so good. To get the meeting point, set the two expressions for y equal to each other:
-x/7 + 3/7 = -2x/15 + 6/15
x = 3
Now use that in either original equation to find that
y = 0
So, the lines intersect at (3,0)
However, you were asked to use an augmented matrix. You start with the matrix of coefficients and work it till the diagonal elements on the left are all zero, except for 1's on the main diagonal:
1 7 3
2 15 6
subtract twice the top row from the bottom row:
1 7 3
0 1 0
subtract 7 times row 2 from row 1:
1 0 3
0 1 0
That is equivalent to the system of equations
x = 3
y = 0