To find the number of solutions to this system of equations, we can solve the system and see if there is a unique solution or if the equations are dependent and have infinitely many solutions, or if they are inconsistent and have no solution.
First, let's solve the system of equations by using substitution or elimination method.
From the first equation, 3x = -12y + 15, we can divide both sides of the equation by 3 to get x = -4y + 5.
Substituting this value of x in the second equation, we get (-4y + 5) + 4y = 5.
Simplifying the equation, we have -4y + 5 + 4y = 5.
The -4y and 4y terms cancel each other out, and we are left with 5 = 5.
This equation is true, which means that both equations in the system are dependent and represent the same line. Therefore, there are infinitely many solutions to this system of equations.
In conclusion, the system has infinitely many solutions.
How many solutions does the system of equations have? 3x = –12y + 15 and x + 4y = 5
1 answer
1 answer