Solve the simultaneous equation
P^2-Q^2=40
Q+P=10
Using the substitution method
Q = 10-P
so,
P^2-Q^2 = 40
P^2-(10-P)^2 = 40
20P-100 = 40
20P = 140
P = 7
So, Q = 3
check: 7^2-3^2 = 49-9 = 40
Thanks for your support steve
To solve the given simultaneous equations using the substitution method, we can follow these steps:
Step 1: Solve one equation for one variable in terms of the other variable.
In the second equation, we have Q + P = 10. We can rearrange this equation to solve for one variable. Let's solve for Q:
Q = 10 - P
Step 2: Substitute the expression for the solved variable back into the other equation.
In the first equation, we have P^2 - Q^2 = 40. Substitute the value of Q from Step 1 into this equation:
P^2 - (10 - P)^2 = 40
Step 3: Simplify and expand the equation.
Expand the squared term:
P^2 - (100 - 20P + P^2) = 40
Simplify the equation:
P^2 - 100 + 20P - P^2 = 40
Combine like terms:
20P - 100 = 40
Step 4: Solve the equation for the remaining variable.
Add 100 to both sides of the equation:
20P = 140
Divide both sides by 20:
P = 7
Step 5: Substitute the value of the solved variable into one of the original equations to find the value of the other variable.
Using the second equation Q + P = 10, substitute the value of P from Step 4:
Q + 7 = 10
Subtract 7 from both sides of the equation:
Q = 10 - 7
Simplify:
Q = 3
So, the solution to the simultaneous equations P^2 - Q^2 = 40 and Q + P = 10 using the substitution method is P = 7 and Q = 3.