Final answer:
To solve the equations x + y = 14 and 7x - 3y = 18, we can use the method of substitution. By substituting the expression for x in terms of y into the second equation, we can solve for y. Substituting the found value of y back into one of the original equations will give us the value of x. Therefore, the solution is x = 6 and y = 8.
Step-by-step explanation:
To find the solution to the equations x + y = 14 and 7x - 3y = 18, we will use the method of substitution.
Step 1: Solve one equation for one variable (in terms of the other variable).
From the first equation, we can solve for x in terms of y: x = 14 - y
Step 2: Substitute the expression for the variable into the other equation.
Substituting 14 - y for x in the second equation, we get: 7(14 - y) - 3y = 18
Step 3: Solve the resulting equation for the remaining variable.
Simplifying the equation, we have: 98 - 7y - 3y = 18
Combining like terms, we get: 98 - 10y = 18
Subtracting 98 from both sides, we have: -10y = -80
Dividing both sides by -10, we get: y = 8
Step 4: Substitute the found value back into one of the original equations to solve for the other variable.
Using the first equation, we have: x + 8 = 14
Subtracting 8 from both sides, we get: x = 6
Therefore, the solution to the given equations is x = 6 and y = 8.