Question

determining the solution
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 + 3(3) = 7 )
2. write the solution as an ordered pair ( (quad, quad) )

Explanation:

Step1: Solve for x using y=3

$x + 3(3) = 7$

Step2: Simplify and isolate x

$x + 9 = 7$
$x = 7 - 9$
$x = -2$

Step3: Form ordered pair (x,y)

Use $x=-2$ and $y=3$

Answer:

$(-2, 3)$