Here are the solutions for your equations. You have to graph them to decide if the lines are perpendicular. I myself think they will criss cross. This is how you plot them:
ContourPlot[{7 y = 21 + 9x, -3y = -24 + x}, {x, 71/34, 139/34}, {y, 203/34, 271/34}]
Solve the following system:
{7 y = 9 x+21 | (equation 1)
-3 y = x-24 | (equation 2)
Express the system in standard form:
{-(9 x)+7 y = 21 | (equation 1)
-x-3 y = -24 | (equation 2)
Subtract 1/9 × (equation 1) from equation 2:
{-(9 x)+7 y = 21 | (equation 1)
0 x-(34 y)/9 = (-79)/3 | (equation 2)
Multiply equation 2 by -9:
{-(9 x)+7 y = 21 | (equation 1)
0 x+34 y = 237 | (equation 2)
Divide equation 2 by 34:
{-(9 x)+7 y = 21 | (equation 1)
0 x+y = 237/34 | (equation 2)
Subtract 7 × (equation 2) from equation 1:
{-(9 x)+0 y = (-945)/34 | (equation 1)
0 x+y = 237/34 | (equation 2)
Divide equation 1 by -9:
{x+0 y = 105/34 | (equation 1)
0 x+y = 237/34 | (equation 2)
Collect results:
Answer: |
| {x = 105/34
y = 237/34