Question Four
x - 7y = 15
-3x + 21y = - 45
The 2nd equation is the 1st equation multiplied by -3. So, they are the same line, and there are infinitely many solutions.
To find the solution to the given system of equations, we can use the method of substitution or elimination.
Let's start by using the method of elimination:
1. Multiply equation 1 by 3 to make the coefficient of x in both equations the same:
3(x - 7y) = 3(15)
3x - 21y = 45
2. Add equation 2 and the modified equation 1 together to eliminate x:
(-3x + 21y) + (3x - 21y) = -45 + 45
0 = 0
The result is an identity, 0 = 0, which means the two equations are dependent. In other words, they represent the same line. Therefore, the system has infinitely many solutions, and any values of (x, y) that satisfy one equation will also satisfy the other.
In conclusion, there are infinitely many solutions to the system of equations represented by:
x - 7y = 15
-3x + 21y = -45