Can some one show me how to use the Substitution method to solve the system of these equations.
x + y = -4
x - y = 2
x + y = 10
y = x + 8
on the first set.
Solve for either x or y in either equation, then put that value into the other equation.
Example:
x + y = -4
x - y = 2
solve for x in the first:
x= -y-4
Put it in the second then..
-y-4 -y=2
-2y=6
y=-3
then solve for x..
x=-y-4=-1
To use the Substitution method, follow these steps:
Step 1: Choose one of the equations and solve for either variable (x or y) in terms of the other variable.
For the first set of equations:
x + y = -4
x - y = 2
Let's solve for x in the first equation:
x = -y - 4
Step 2: Substitute the value of the variable you solved for in Step 1 into the other equation.
Using the second equation:
x - y = 2
Substitute x = -y - 4:
(-y - 4) - y = 2
Step 3: Solve the resulting equation for the remaining variable.
Simplifying the equation:
-y - 4 - y = 2
-2y - 4 = 2
-2y = 6
Divide by -2:
y = -3
Step 4: Substitute the value of y back into one of the original equations to solve for the other variable.
Using the first equation:
x + y = -4
Substitute y = -3:
x + (-3) = -4
x - 3 = -4
Add 3 to both sides:
x = -1
So the solution to the first set of equations is x = -1 and y = -3.
Now, let's go through the same steps for the second set of equations:
Step 1: Solve for y in terms of x in the second equation:
y = x + 8
Step 2: Substitute y = x + 8 into the first equation:
x + y = 10
x + (x + 8) = 10
Step 3: Simplify the equation:
2x + 8 = 10
Subtract 8 from both sides:
2x = 2
Divide by 2:
x = 1
Step 4: Substitute the value of x back into one of the original equations to solve for y.
Using the second equation:
y = x + 8
y = 1 + 8
y = 9
So the solution to the second set of equations is x = 1 and y = 9.
That's how you use the Substitution method to solve a system of equations.