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