Solving Systems of Equations Using Substitution

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

• $y = 4x + 1$

• $2y - 4x = 14$

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, which involves replacing one variable with its equivalent expression from 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 the expression for $y$ from the first equation into the second equation: $2y - 4x = 14$ becomes $2(4x + 1) - 4x = 14$.

3. Expand the equation: $2 \times 4x + 2 \times 1 - 4x = 14$.

4. Simplify the equation by combining like terms.

Try solving on your own before revealing the answer!

Final Answer:

$x = 2$, $y = 9$

After substituting and simplifying, you solve for $x$ and then use that value to find $y$ using the first equation.