Question

L1 : 2(x-1)-3(y-3)=0
L2 : 3(x+2)-(y-7)=20

Answer 1

L1 and L2 intersect.

Answer 2

Equation 1.

2 ( x - 1 ) - 3 ( y - 3 ) = 0

2 x - 2 - 3 y + 9 = 0

2 x - 3 y + 7 = 0

Subtract 7 to both sides

2 x - 3 y = - 7

Equation 2.

3 ( x + 2 ) - ( y - 7 ) = 20

3 x + 6 - y + 7 = 20

3 x - y + 13 = 20

Subtract 13 to both sides

3 x - y = 7

Now you must solve sytem.

2 x - 3 y = - 7

3 x - y = 7
__________

Mutiply first equation by - 1.5

- 3 x + 4.5 y = 10.5

Add up the equations:

- 3 x + 4.5 y = 10.5
+
3 x - y = 7
_______________

- 3 x + 3 x + 4 .5 y - y = 10.5 + 7

3.5 y = 17.5

y = 17.5 / 3.5

y = 5

Put this value in equation 3 x - y = 7

3 x - 5 = 7

Add 5 to both sides

3 x = 12

x = 4