Graph of Parallel lines shows a system of equations with no solutions
Step-by-step explanation:
Consider a set of equations
[tex]7x - 2y = 16\\21x + 6y =24[/tex]
If we solve this both equations using any one of the solving method, (Substitution method) then we will get
[tex]7x-2y=16\\7x=16+2y\\x=\frac{16+2y}{7}[/tex]
substituting the following x in 2nd equation (21x + 6y = 24) We get
[tex]21(\frac{16+2y}{7} )+6y=24\\3(16+2y)+6y=24\\48+6y+6y=24\\12y=24-48\\y=-\frac{24}{12} \\y=-2[/tex]
Put y= -2 in x equation
[tex]x=\frac{16+2(-2)}{7}\\ x=\frac{16-4}{7}\\\x=\frac{12}{7} \\x=1.71[/tex]
Comparing these (x,y) values we can understand that they never meet at a point
