Solving a System of Equations Using Substitution

Q1. Solve the system of equations by the substitution method:

$\begin{cases} y = 4x + 1 \\ 2y - 4x = 14 \end{cases}$

Background

Topic: Systems of Linear Equations (Substitution Method)

This question tests your ability to solve a system of two linear equations using the substitution method. This method involves solving one equation for one variable and substituting that expression into the other equation.

Key Terms and Formulas

• System of equations: Two or more equations with the same variables.

• Substitution method: Solve one equation for one variable, then substitute that expression into the other equation.

Step-by-Step Guidance

1. Notice that the first equation is already solved for $y$: $y = 4x + 1$.

2. Substitute $y = 4x + 1$ into the second equation $2y - 4x = 14$.

3. Replace $y$ in the second equation: $2(4x + 1) - 4x = 14$.

4. Expand the equation: $8x + 2 - 4x = 14$.

5. Combine like terms to isolate $x$ on one side of the equation.

Try solving on your own before revealing the answer!