Using the Substitution method solve
7x+5y=-23
-6x+y=25
from the second equation:
y=25+6x
put that in the first equation
7x+5(25+6x)=-23
solve for x
I am confused how you would get an order pair from that....can you help?
To solve the system of equations using the substitution method, follow these steps:
Step 1: Solve one of the equations for one variable in terms of the other variable.
Let's solve the second equation (-6x + y = 25) for y:
y = 6x + 25
Step 2: Substitute the expression obtained in Step 1 into the other equation.
Now, substitute the value of y from Step 1 into the first equation (7x + 5y = -23):
7x + 5(6x + 25) = -23
Step 3: Solve the resulting equation.
7x + 30x + 125 = -23
37x + 125 = -23
37x = -23 - 125
37x = -148
x = -148 / 37
x = -4
Step 4: Substitute the value of x obtained in Step 3 into one of the original equations.
Let's substitute x = -4 into the second equation (-6x + y = 25):
-6(-4) + y = 25
24 + y = 25
y = 25 - 24
y = 1
Step 5: Check the solution in both original equations.
Substituting x = -4 and y = 1 into the first equation (7x + 5y = -23):
7(-4) + 5(1) = -23
-28 + 5 = -23
-23 = -23 (True)
Substituting x = -4 and y = 1 into the second equation (-6x + y = 25):
-6(-4) + 1 = 25
24 + 1 = 25
25 = 25 (True)
Therefore, the solution to the system of equations is x = -4 and y = 1.