Solve the System of Equations by the Substitution Method

Video Explanation

Question

Solve the following system of equations by the substitution method:

\[ 0.4x + 0.3y = 1.7, \\ 0.7x – 0.2y = 0.8 \]

Solution

Step 1: Remove Decimals

Multiply both equations by 10:

\[ 4x + 3y = 17 \quad \text{(1)} \]

\[ 7x – 2y = 8 \quad \text{(2)} \]

Step 2: Express One Variable in Terms of the Other

From equation (2):

\[ -2y = 8 – 7x \]

\[ y = \frac{7x – 8}{2} \quad \text{(3)} \]

Step 3: Substitute in Equation (1)

Substitute equation (3) into equation (1):

\[ 4x + 3\left(\frac{7x – 8}{2}\right) = 17 \]

Multiply both sides by 2:

\[ 8x + 21x – 24 = 34 \]

\[ 29x = 58 \]

\[ x = 2 \]

Step 4: Find the Value of y

Substitute \(x = 2\) into equation (3):

\[ y = \frac{7(2) – 8}{2} \]

\[ y = \frac{6}{2} = 3 \]

Conclusion

The solution of the given system of equations is:

\[ x = 2,\quad y = 3 \]

\[ \therefore \quad \text{The solution is } (2,\; 3). \]