Solve the System of Equations by the Substitution Method

Video Explanation

Question

Solve the following system of equations by the substitution method:

\[ 3x – 7y + 10 = 0, \\ y – 2x – 3 = 0 \]

Solution

Step 1: Write the Equations in Standard Form

\[ 3x – 7y = -10 \quad \text{(1)} \]

\[ y – 2x = 3 \quad \text{(2)} \]

Step 2: Express One Variable in Terms of the Other

From equation (2):

\[ y = 2x + 3 \quad \text{(3)} \]

Step 3: Substitute in Equation (1)

Substitute equation (3) into equation (1):

\[ 3x – 7(2x + 3) = -10 \]

\[ 3x – 14x – 21 = -10 \]

\[ -11x = 11 \]

\[ x = -1 \]

Step 4: Find the Value of y

Substitute \(x = -1\) into equation (3):

\[ y = 2(-1) + 3 \]

\[ y = 1 \]

Conclusion

The solution of the given system of equations is:

\[ x = -1,\quad y = 1 \]

\[ \therefore \quad \text{The solution is } (-1,\; 1). \]