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Quick intersection question , please help (AS)

Hello,

The line AB has equation 3x þ 5y ¼ 8 and the point A has coordinates (6,2).

b) The line AB intersects the line with equation 2x þ 3y ¼ 3 at the point B. Find the
coordinates of B.

The answer is "Eliminating x or y (unsimplified)
x = −9
y = 7"

Please could someone help me with the method, and how to get this answer. As all of my attempts keep coming up with the wrong answer.

Thank you very much

Reply 1

Mr M

Study Forum Helper

Multiply the first equation by 2.

Multiply the second equation by 3.

Subtract the second equation from the first equation.

Now use the value of y you have obtained to find x by substituting it back into one of the original equations.