Solve using the substitution method and state if the system has a solution.
4p-2q=16
5p+7q=1
4p - 2q = 16
4p = 16 + 2q
p = 4 + .5q
5p + 7q = 1
Substitute 4 + .5q for p in the last equation and solve for q. Put that value in the previous equation to find p. Check by putting both values into the last equation.
solve the system of equations answer as an ordered pair 5x-y=27
To solve this system of equations using the substitution method, follow the steps below:
1. Solve one of the equations for one variable in terms of the other variable. Let's solve the first equation for p:
4p - 2q = 16
Adding 2q to both sides:
4p = 2q + 16
Dividing by 4:
p = (2q + 16)/4
Simplifying further:
p = 0.5q + 4
2. Substitute the expression for p into the other equation.
Substituting p = 0.5q + 4 into the second equation:
5(0.5q + 4) + 7q = 1
Multiplying:
2.5q + 20 + 7q = 1
Combining like terms:
9.5q + 20 = 1
3. Solve the resulting equation for q:
Subtracting 20 from both sides:
9.5q = 1 - 20
9.5q = -19
Dividing by 9.5:
q = -19/9.5
q = -2
4. Substitute the value of q back into the expression for p to find its value:
p = 0.5q + 4
p = 0.5(-2) + 4
p = -1 + 4
p = 3
5. Therefore, the solution to the system of equations is p = 3 and q = -2.
Regarding whether the system has a solution, since we were able to find specific values for both p and q, we can conclude that the system does have a solution.