solve by substitution method
x^2=y^2+39
x-y=3
If x - y = 3, then x = y + 3
Substitute y + 3 for x in the first equation and solve for y. Put that value into the second equation to find x. To check, put both values back into the first equation.
I hope this helps. Thanks for asking.
To solve the system of equations using 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, x - y = 3, for x in terms of y.
Add y to both sides of the equation:
x = 3 + y
Step 2: Substitute the expression obtained in step 1 into the other equation.
Substitute x = 3 + y into the first equation, x^2 = y^2 + 39:
(3 + y)^2 = y^2 + 39
Step 3: Expand and simplify the equation obtained in step 2.
Squaring (3 + y) gives:
9 + 6y + y^2 = y^2 + 39
Step 4: Combine like terms and solve for y.
Subtract y^2 from both sides:
9 + 6y = 39
Step 5: Simplify and isolate y.
Subtract 9 from both sides:
6y = 30
Step 6: Solve for y.
Divide both sides by 6:
y = 5
Step 7: Substitute the value of y back into one of the original equations to solve for x.
Using the second equation, x - y = 3, substitute y = 5:
x - 5 = 3
Step 8: Solve for x.
Add 5 to both sides:
x = 8
Therefore, the solution to the system of equations is x = 8 and y = 5.