where does two lines intersect

Question

solve the following pairs of simultaneous equation;

5x–3y=2

6x+7y=13

find the cordinate of their intersection with x and y

Answer 1

5x-3y=2

6x+7y=13

multiply all terms on both sides of the first equation by 6

multiply all terms on both sides of the second equation by 5

6(5x)-6(3y)=6(2)

30x-18y=12

5(6x)+5(7y)=5(13)

30x+35y=65

30x-18y=12

subtract the second equation from the first

      53y=53

          y=1

substitute 1 for y in either original equation

5x-3y=2

5x-3(1)=2

5x-3=2

5x=5

x=1

solution:(1,1)