- #1
santa
- 18
- 0
find a and r
[tex]a+ar+ar^2=7[/tex]
[tex]a^3+a^3r^3+a^3r^6=73[/tex]
[tex]a+ar+ar^2=7[/tex]
[tex]a^3+a^3r^3+a^3r^6=73[/tex]
santa said:find a and r
[tex]a+ar+ar^2=7[/tex]
[tex]a^3+a^3r^3+a^3r^6=73[/tex]
The general approach to solving a system of equations is to isolate one variable in one equation and substitute it into the other equation. This will create a single equation with one variable, which can then be solved for that variable. The solution can then be substituted back into either of the original equations to find the other variable.
In this system of equations, we can see that the first equation has a common factor of "a" in all three terms, while the second equation has a common factor of "a^3" in all three terms. Therefore, it would be most efficient to isolate "a" in the first equation and "a^3" in the second equation.
Yes, the substitution method can be used to solve this system of equations. As mentioned earlier, we can isolate one variable and substitute it into the other equation to create a single equation with one variable.
Yes, you can check your solution by substituting the values back into the original equations. If the solution is correct, it should satisfy both equations.
Yes, there are two special cases for this system of equations. The first case is when r = 1, which would make both equations equivalent to a + a + a = 7 and a^3 + a^3 + a^3 = 73. In this case, the solution would be a = 7/3 and r = 1. The second case is when r = -1, which would make the first equation equivalent to a - a + a = 7 and the second equation equivalent to a^3 - a^3 + a^3 = 73. In this case, the solution would be a = 7 and r = -1.