Question

What point is interected between 10x-3y=19 and 5x+4y=-7

Answer 1

(1, -3)

Explanation:

Solve the system of equations of the two lines:

10x-3y=19 ------> eq 1

5x+4y=-7 --------> eq 2

Solve by elimination:

eq 2 x 2

2( 5x+4y) = 2(-7 )

10x + 8y = - 14 ------> eq 3

eq3 - eq 1:

(10x + 8y) - (10x-3y) = - 14 - 19

10x + 8y - 10x + 3y = -33

8y + 3y = -33

11y = -33

y = -3 (substitute back into eq 1)

10x - 3y = 19

10x - 3(-3) = 19

10x + 9 = 19

10x = 19 - 9

10x = 10

x = 1

Hence the intersection point is (1, -3)