The difference of two numbers is 7. The sum of the numbers is -1. What are the numbers?
I've come up with two equations:
x-y=7 and x+y=-1 but don't know what to figure it out from there since there are no numbers on the left side of the equation to work with.
To solve this system of equations, you can use a method called substitution. Let me explain the steps to find the values of x and y.
Step 1: Start with the given equations:
x - y = 7 ..... Equation 1
x + y = -1 ..... Equation 2
Step 2: Solve Equation 2 for x:
x = -1 - y ..... Rewrite Equation 2
Step 3: Substitute the value of x from Step 2 into Equation 1:
-1 - y - y = 7 ..... Substitute -1 - y for x in Equation 1
Step 4: Simplify and solve for y:
-2y - 1 = 7
-2y = 7 + 1
-2y = 8
y = 8 / -2
y = -4
Step 5: Substitute the value of y = -4 into Equation 2 to find x:
x + (-4) = -1
x - 4 = -1
x = -1 + 4
x = 3
So the solution to the system of equations is x = 3 and y = -4. Therefore, the two numbers are 3 and -4.