Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations, where \(x \ne 0\) and \(y \ne 0\): \[ x + y = 2xy, \\ \frac{x – y}{xy} = 6 \] Solution Step 1: Simplify the Second Equation \[ \frac{x – y}{xy} = 6 \] \[ \frac{x}{xy} […]

Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations, where \(x \ne 0,\; y \ne 0\): \[ x + y = 5xy, \\ x + 2y = 13xy \] Solution Step 1: Divide Each Equation by \(xy\) From the first equation: \[ \frac{x}{xy} + \frac{y}{xy} =

Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations, where \(x \ne -1\) and \(y \ne 1\): \[ \frac{5}{x+1} – \frac{2}{y-1} = \frac{1}{2}, \\ \frac{10}{x+1} + \frac{2}{y-1} = \frac{5}{2} \] Solution Step 1: Make Suitable Substitution Let \[ \frac{1}{x+1} = a,\quad \frac{1}{y-1} = b \] Then

Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations: \[ \frac{1}{2(x+2y)} + \frac{5}{3(3x-2y)} = -\frac{3}{2}, \\ \frac{5}{4(x+2y)} – \frac{3}{5(3x-2y)} = \frac{61}{60} \] Solution Step 1: Make Suitable Substitution Let \[ \frac{1}{x+2y} = a,\quad \frac{1}{3x-2y} = b \] Then the given equations become: \[ \frac{a}{2} + \frac{5b}{3}

Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations: \[ \frac{3}{x+y} + \frac{2}{x-y} = 2, \\ \frac{9}{x+y} – \frac{4}{x-y} = 1 \] Solution Step 1: Make Suitable Substitution Let \[ \frac{1}{x+y} = a,\quad \frac{1}{x-y} = b \] Then the given equations become: \[ 3a + 2b

Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations: \[ \frac{5}{x+y} – \frac{2}{x-y} = -1, \\ \frac{15}{x+y} + \frac{7}{x-y} = 10 \] Solution Step 1: Make Suitable Substitution Let \[ \frac{1}{x+y} = a,\quad \frac{1}{x-y} = b \] Then the given equations become: \[ 5a – 2b

Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations: \[ \frac{22}{x+y} + \frac{15}{x-y} = 5, \\ \frac{55}{x+y} + \frac{45}{x-y} = 14 \] Solution Step 1: Make Suitable Substitution Let \[ \frac{1}{x+y} = a,\quad \frac{1}{x-y} = b \] Then the given equations become: \[ 22a + 15b

Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations, where \(x+y \ne 0\) and \(x-y \ne 0\): \[ \frac{xy}{x+y} = \frac{6}{5}, \\ \frac{xy}{y-x} = 6 \] Solution Step 1: Remove Denominators From the first equation: \[ \frac{xy}{x+y} = \frac{6}{5} \] \[ 5xy = 6(x+y) \quad \text{(1)}

Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations, where \(x+y \ne 0\) and \(x-y \ne 0\): \[ \frac{6}{x+y} = \frac{7}{x-y} + 3, \\ \frac{1}{2(x+y)} = \frac{1}{3(x-y)} \] Solution Step 1: Solve the Second Equation \[ \frac{1}{2(x+y)} = \frac{1}{3(x-y)} \] Cross-multiplying, \[ 3(x-y) = 2(x+y) \]

Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations, where \(x \ne 0,\; y \ne 0\): \[ \frac{2}{x} + \frac{3}{y} = \frac{9}{xy}, \\ \frac{4}{x} + \frac{9}{y} = \frac{21}{xy} \] Solution Step 1: Remove Denominators Multiply both equations by \(xy\): \[ 2y + 3x = 9 \quad