Graph the following system of equations:

1. [tex]4x + y = 8[/tex]
2. [tex]x + 3y = 8[/tex]

s t an d a r d l in e a r e q u a t i o n : y = a x + b { 4 x + y = 8 ∣ s u b t r a c t 4 x t o b o t h s i d es x + 3 y = 8 ∣ s u b t r a c t x t o b o t h s i d es ​ { y = − 4 x + 8 3 y = − x + 8 ∣ d i v i d e e a c h t er m b y 3 ​
{ y = − 4 x + 8 y = − 3 1 ​ x + 3 8 ​ ​ y = − 4 x + 8 T o f in d t h e x − a x i s in t ersec t i o n p o in t , se t y e q u a l t o zero an d so l v e f or x : y = 0 → 0 = − 4 x + 8 4 x = 8 ∣ d i v i d e b o t h s i d es b y 4 x = 2 p o in t : ( 2 , 0 )
T o f in d t h e y − a x i s in t ersec t i o n p o in t , se t x e q u a l t o zero an d so l v e f or y : x = 0 → y = − 4 ⋅ 0 + 8 y = 8 p o in t : ( 0 , 8 )
y = − 3 1 ​ x + 3 8 ​ t h e x − a x i s in t ersec t i o n p o in t y = 0 → 0 = − 3 1 ​ x + 3 8 ​ 3 1 ​ x = 3 8 ​ ∣ m u lt i pl y b o t h s i d es b y 3 x = 8 p o in t : ( 8 , 0 )
t h e y − a x i s in t ersec t i o n p o in t x = 0 → y = − 3 1 ​ ⋅ 0 + 3 8 ​ y = 3 8 ​ p o in t : ( 0 , 3 8 ​ )
A n s w er : { y = − 4 x + 8 ∣ m u lt i pl y e a c h t er m b y ( − 3 ) 3 y = − x + 8 ​ { − 3 y = 12 x − 24 3 y = − x + 8 ​ + − − − − − − − 0 = 11 x − 16 11 x = 16 ∣ d i v i d e b o t h s i d es b y 11 x = 11 16 ​
y = − 4 ⋅ 11 16 ​ + 8 y = − 11 64 ​ + 11 88 ​ y = 11 24 ​ { x = 11 16 ​ y = 11 24 ​ ​

Answered by Lilith | 2024-06-10

To graph the system of equations, convert them into slope-intercept form and identify their intercepts. The intersection point, which represents the solution to the system, is ( 11 16 ​ , 11 24 ​ ) . Plot these lines on a graph to accurately visualize their intersection.
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Answered by Lilith | 2024-12-26