Solve the following sequence systems algebraic ally
x+2y=17
x-y=2
since x=y+2,
(y+2)+2y=17
...
an executive rents a car for $50 plus $35 a day. if she is charged $190, how many days did she keep the car?
50+35x = 190
To solve the sequence of linear equations algebraically, you can use the method of substitution or the method of elimination. Let's solve it using the method of substitution.
Step 1: Solve one equation for one variable in terms of the other variable.
From the second equation, we have x = y + 2.
Step 2: Substitute the expression for the variable found in step 1 into the other equation.
Substitute x = y + 2 into the first equation:
(y + 2) + 2y = 17.
Step 3: Simplify and solve for y.
Simplifying the equation:
y + 2 + 2y = 17,
3y + 2 = 17,
3y = 15,
y = 5.
Step 4: Substitute the value of y back into one of the original equations to solve for x.
Using the first equation:
x + 2(5) = 17,
x + 10 = 17,
x = 7.
Step 5: Check if the solution satisfies the original equations.
Substitute the values of x and y into the original equations. Both equations hold true:
7 + 2(5) = 17,
17 = 17.
Therefore, the solution to the given sequence of equations is x = 7 and y = 5.