Question

Solve the system of equations by the substitution method.

y = x + 9x + 5
?
y = -x + 11x + 29
Select the correct choice below and, if necessary, fill in the answer box to complete
O A. The solution set is {
(Type an ordered pair. Use a comma to separate answers if needed.)
OB. There is no solution.

Answer 1

B. There is no solution.

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Equality Properties

Algebra I

• Solving systems of equations using substitution/elimination
• Solving systems of equations by graphing

Explanation:

Step 1: Define systems

y = x + 9x + 5

y = -x + 11x + 29

Step 2: Simplify systems

y = 10x + 5

y = 10x + 29

Step 3: Solve for x

Substitution

1. Substitute in y: 10x + 5 = 10x + 29
2. Subtract 10x on both sides: 5 ≠ 29

Here we see that 5 does not equal 29.

∴ The systems has no solutions.

Step 4: Graph systems

Check the solution set (if applicable).

We see that the 2 lines are parallel and will never intersect. Therefore, this proves that our systems has no solution.