Question

find the solution to the system of equations, ( x + 3y = 7 ) and ( 2x + 4y = 8 ).

1. isolate ( x ) in the first equation: ( x = 7 - 3y )
2. substitute the value for ( x ) into the second equation: ( 2(7 - 3y) + 4y = 8 )
3. solve for ( y ):

( 14 - 6y + 4y = 8 )
( 14 - 2y = 8 )
( -2y = -6 )
( y = 3 )

1. substitute ( y ) into either original equation: ( x = 7 - 3(3) )
2. write the solution as an ordered pair: ( , )

Explanation:

Step1: Calculate x value

We know \( y = 3 \), substitute into \( x = 7 - 3y \). So \( x=7 - 3\times3=7 - 9=- 2 \).

Step2: Form ordered pair

An ordered pair is in the form \((x,y)\), we have \( x=-2 \) and \( y = 3 \), so the ordered pair is \((-2,3)\).

Answer:

\((-2, 3)\)