Question

Solve the system of equations by the addition method
5x – 3y = 4
7x-2y = 4

Answer 1

x = 4/11, y = -8/11 or (4/11,-8/11)

Answer 2

`(x,y)= > ((4)/(11),-(8)/(11))` or
`(x,y)= > (0.36,-0.72)`

Explanation:

Addition method, is also known as the Elimination method.

`\left \{ {{5x-3y=4} \atop {7x-2y=4}} \right.\\\\\left \{ {-2({5x-3y=4}) \atop 3({7x-2y=4})} \right.\\\\\left \{ {{-10x+6y=-8} \atop {21x-6y=12}} \right.\\\\11x=4\\\\(11x)/(11) =(4)/(11)\\\\x = (4)/(11)`

`5x-3y=4`

`5((4)/(11)) -3y=4\\\\(20)/(11) -3y=4\\\\11((20)/(11) -3y=4)\\\\20-33y=44\\\\-20 -20\\\\-33y=24\\\\/-33 /-33\\\\y = (24)/(-33) =(8)/(-11)\\\\y=-(8)/(11)`

`(x,y)= > ((4)/(11),-(8)/(11))` or
`(x,y)= > (0.36,-0.72)`

Hope this helps!