Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations: \[ \frac{1}{7x} + \frac{1}{6y} = 3, \\ \frac{1}{2x} – \frac{1}{3y} = 5 \] Solution Step 1: Make Suitable Substitution Let \[ \frac{1}{x} = a,\quad \frac{1}{y} = b \] Then the given equations become: \[ \frac{a}{7} + \frac{b}{6} […]

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 =

Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations, where \(y \ne 0\): \[ 2x – \frac{3}{y} = 9, \\ 3x + \frac{7}{y} = 2 \] Solution Step 1: Express One Variable in Terms of the Other From the first equation: \[ 2x – \frac{3}{y} =

Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations: \[ 3x – \frac{y+7}{11} + 2 = 10, \\ 2y + \frac{x+11}{7} = 10 \] Solution Step 1: Simplify Both Equations First equation: \[ 3x – \frac{y+7}{11} + 2 = 10 \] \[ 3x – \frac{y+7}{11} =

Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations: \[ \sqrt{2}x – \sqrt{3}y = 0, \\ \sqrt{3}x – \sqrt{8}y = 0 \] Solution Step 1: Express One Variable in Terms of the Other From the first equation: \[ \sqrt{2}x – \sqrt{3}y = 0 \] \[ \sqrt{2}x

Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations: \[ x + 2y = \frac{3}{2}, \\ 2x + y = \frac{3}{2} \] Solution Step 1: Express One Variable in Terms of the Other From the first equation: \[ x + 2y = \frac{3}{2} \] \[ x

Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations: \[ x + \frac{y}{2} = 4, \\ \frac{x}{3} + 2y = 5 \] Solution Step 1: Remove Fractions Multiply the first equation by 2: \[ 2x + y = 8 \quad \text{(1)} \] Multiply the second equation

Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations: \[ \frac{4}{x} + 3y = 8, \\ \frac{6}{x} – 4y = -5 \] Solution Step 1: Express One Variable in Terms of the Other From the first equation: \[ \frac{4}{x} + 3y = 8 \] \[ 3y

Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations: \[ \frac{x}{3} + \frac{y}{4} = 11, \\ \frac{5x}{6} – \frac{y}{3} = -7 \] Solution Step 1: Remove Fractions Multiply the first equation by 12: \[ 4x + 3y = 132 \quad \text{(1)} \] Multiply the second equation

Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations: \[ \frac{x}{7} + \frac{y}{3} = 5, \\ \frac{x}{2} – \frac{y}{9} = 6 \] Solution Step 1: Remove Fractions Multiply the first equation by 21: \[ 3x + 7y = 105 \quad \text{(1)} \] Multiply the second equation