GMATPrepNow wrote:
On the x-y coordinate plane, lines j and k intersect at one point.
If the equation of line j is bx + ay = 5, and the equation of line k is 2bx - 3ay = -5, what is the value of a + b?
(1) Lines j and k intersect at (1, -3).
(2) a - b = -3
*kudos for all correct solutions
Statement 1 :- Lines j and k intersect at (1, -3).Use (1,-3) in the two given equation .
1st Equation:- bx + ay = 5
b - 3a = 5.
2nd Equation:- 2bx - 3ay = -5
2b(1) - 3a(-3) = -5
2b + 9a = -5.
Both the equation are in terms of a & b. On solving we can get the values of a & b.
Hence Sufficient.
Statement 2 :- a - b = -3.a - b = -3
a = b+3.
1st Equation:- bx + ay = 5.
bx + (b+3)y = 5.
bx + by + 3y = 5.
2nd Equation:- 2bx - 3ay = -5
2bx - 3y(b+3) = -5
2bx - 3by -9y = -5
As you can see, we couldn't convert these two equation in two variable.
We have three unknown variable (x, b & y).
So we need three equation to find the values of a & b, thus a+b.
Hence Insufficient.
Ans - A.