Solve the System of Equations by the Substitution Method

Video Explanation

Question

Solve the following system of equations:

\[ 0.5x + 0.7y = 0.74, \\ 0.3x + 0.5y = 0.5 \]

Solution

Step 1: Remove Decimals

Multiply both equations by 10:

\[ 5x + 7y = 7.4 \quad \text{(1)} \]

\[ 3x + 5y = 5 \quad \text{(2)} \]

Step 2: Express One Variable in Terms of the Other

From equation (2):

\[ 3x + 5y = 5 \]

\[ 5y = 5 – 3x \]

\[ y = 1 – 0.6x \quad \text{(3)} \]

Step 3: Substitute in Equation (1)

Substitute equation (3) into equation (1):

\[ 5x + 7(1 – 0.6x) = 7.4 \]

\[ 5x + 7 – 4.2x = 7.4 \]

\[ 0.8x = 0.4 \]

\[ x = 0.5 \]

Step 4: Find the Value of y

Substitute \(x = 0.5\) into equation (3):

\[ y = 1 – 0.6(0.5) \]

\[ y = 1 – 0.3 = 0.7 \]

Conclusion

The solution of the given system of equations is:

\[ x = 0.5,\quad y = 0.7 \]

\[ \therefore \quad \text{The solution is } (0.5,\; 0.7). \]