Solve uing the subtitution method. Show your work. If the system has no solution or an infinite number of solutions, stat this,3x-15y=-12
3x+24y=-12
3x-15y=-12 ...(1)
3x+24y=-12 ...(2)
Subtract (1) from (2) to get
39y=0, or y=0.
Substitute into (1) and get
3x+0=-12,
or x=-4
To solve the given system of equations using the substitution method, we will solve one equation for one variable and substitute it into the other equation.
Let's start with the first equation: 3x - 15y = -12. We can rearrange this equation to solve for x:
3x = 15y - 12
x = (15y - 12) / 3
x = 5y - 4
Now, substitute this value of x into the second equation: 3x + 24y = -12:
3(5y - 4) + 24y = -12
15y - 12 + 24y = -12
39y - 12 = -12
39y = 0
y = 0
Substitute the value of y back into the first equation to find x:
x = 5(0) - 4
x = -4
Therefore, the solution to the system of equations is x = -4 and y = 0.
In this case, the system has a unique solution, and we have successfully solved it using the substitution method.