I need help solving this using the substitution method
4p-2q= 16,
5p + 7q= 1
19-7-5=
Start with one formula.
4p - 2q = 16
Get one variable alone on one side of the equation.
-2q = 16 - 4p
q = 2p - 8
Then substitute the value into the other equation.
5p + 7q = 1
5p + 7(2p - 8)= 1
Solve for p.
Once you find p, put that value into the first equation to solve for q. To check, put both values back into the second equation.
I hope this helps. Thanks for asking.
4 p = 16 + 2 q
so
p = (4 + .5 q)
substitute that value for p in the second equation
5 (4 + .5 q) + 7 q = 1
20 + 2.5 q + 7 q = 1
9.5 q = -19
q = -190/95 = -38/19 =-2
put that back in either first or second equation to solve for p
p = 4 + .5*(-2)
p = 4 - 1 = 3
check
4(3) -2 (-2) = 12 + 4 = 16 check
5(3) + 7(-2) = 15 - 14 = 1 check
To solve this system of equations using the substitution method, we will solve one equation for one variable and then substitute that expression into the other equation.
Let's solve the first equation for p:
4p - 2q = 16
First, add 2q to both sides of the equation:
4p = 2q + 16
Next, divide both sides by 4 to solve for p alone:
p = (2q + 16)/4
p = 0.5q + 4 -- (Equation 1)
Now, substitute this expression for p into the second equation:
5p + 7q = 1
Replace p with 0.5q + 4:
5(0.5q + 4) + 7q = 1
Distribute 5 to each term inside the parentheses:
2.5q + 20 + 7q = 1
Combine like terms:
9.5q + 20 = 1
Next, subtract 20 from both sides of the equation:
9.5q = 1 - 20
9.5q = -19
Finally, divide both sides by 9.5 to solve for q:
q = -19/9.5
q = -2
Now that we have the value of q, we can substitute it back into Equation 1 to find the value of p:
p = 0.5q + 4
p = 0.5(-2) + 4
p = -1 + 4
p = 3
Therefore, the solution to the system of equations is p = 3 and q = -2.