Question

Find the point (x1 , x2 ) that lies on the line x1 + 3x2 = 6 and on the line x1 - x2 = 2.

Answer 1

To find the point (x1, x2) that lies on both lines, x1 + 3x2 = 6 and x1 - x2 = 2, you need to solve the system of equations. The point is (3, 1).

Step-by-step explanation:

To find the point (x1, x2) that lies on both the lines x1 + 3x2 = 6 and x1 - x2 = 2, you need to solve the system of equations. Here's how:

1. Start by isolating x1 in both equations. In the first equation, x1 = 6 - 3x2. In the second equation, x1 = x2 + 2.
2. Set the expressions for x1 equal to each other:
   6 - 3x2 = x2 + 2
3. Now, solve for x2. Subtract x2 from both sides:
   6 - 4x2 = 2
4. Subtract 6 from both sides:
   -4x2 = -4
5. Divide both sides by -4 to isolate x2:
   x2 = 1
6. Substitute the value of x2 back into one of the original equations to find x1. Using the second equation:
   x1 = 1 + 2
7. Calculate x1:
   x1 = 3

The point that lies on the lines x1 + 3x2 = 6 and x1 - x2 = 2 is (3, 1).