Question

4x+y=8 and x+3y=8 graphed

Answer 1

`standard \ linear \ equation\ :\\\\y=ax+b\\\\ \begin{cases} 4x+y=8\ \ |\ subtract\ 4x\ to\ both\ sides\\ x+3y=8 \ \ |\ subtract\ x\ to\ both\ sides \end{cases}\\\\\begin{cases} y=-4x+8 \\ 3y=-x+8\ \ | \ divide \ each \ term \ by \ 3 \end{cases}`


`\begin{cases} y=-4x+8 \\ y=-(1)/(3)x+(8)/(3) \end{cases}\\\\y=-4x+8\\ To \ find \ the \ x-axis \ intersection \ point, \\set \ y \ equal \ to \ zero \ and \ solve \ for \ x : \\ \\y=0 \ \to 0=-4x+8\\\\4x=8 \ \ | \ divide \ both \ sides\ by\ 4 \\\\x=2\\\\ point : \ \ (2,0)`


`To \ find \ the \ y-axis \ intersection \ point, \\set \ x \ equal \ to \ zero \ and \ solve \ for \ y : \\ \\x=0 \ \to y=-4 \cdot 0+8\\ y=8 \\ point: \ \ (0,8)`



`y=-(1)/(3)x+(8)/(3)\\\\ \ the \ x-axis \ intersection \ point \\ \\y=0 \ \to 0=-(1)/(3)x+(8)/(3)\\ (1)/(3)x=(8)/(3) \ \ | \ multiply\ both\ sides\ by\ 3 \\\\x=8 \\\\point: \ \ (8,0)`


`the \ y-axis \ intersection \ point \\ \\x=0 \ \to y=-(1)/(3) \cdot 0+(8)/(3) \\ y=(8)/(3) \\ point : \ \ (0,(8)/(3))`



`Answer :\\\\ \begin{cases} y=-4x+8 \ \ | \ multiply \ each \ term \ by \ (-3) \\ 3y=-x+8 \end{cases}\\\begin{cases} -3y=12x-24 \\ 3y=-x+8 \end{cases}\\+-------\\0=11x-16\\11x=16\ \ | \ divide \ both \ sides\ by\ 11\\x=(16)/(11)`


`y=-4 \cdot (16)/(11)+8 \\ y=- ( 64)/(11)+(88)/(11)\\y= (24)/(11)\\\\\begin{cases} x=(16)/(11) \\ y=(24)/(11) \end{cases}`