solve the system x+y=10, 2x-3y=12. give your answer as an ordered pair (x,y).

Explanation:

Step1: Solve for x from first equation

From ( x + y = 10 ), we get ( x = 10 - y ).

Step2: Substitute x into second equation

Substitute ( x = 10 - y ) into ( 2x - 3y = 12 ):
( 2(10 - y) - 3y = 12 )
Expand: ( 20 - 2y - 3y = 12 )
Simplify: ( 20 - 5y = 12 )
Subtract 20: ( -5y = 12 - 20 = -8 )
Divide by -5: ( y = \frac{8}{5} = 1.6 )

Step3: Find x using y

( x = 10 - y = 10 - \frac{8}{5} = \frac{50 - 8}{5} = \frac{42}{5} = 8.4 )

Answer:

(\left( \frac{42}{5}, \frac{8}{5} \right)) or ((8.4, 1.6))