January 2026

Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations: \[ \frac{1}{3x+y} + \frac{1}{3x-y} = \frac{3}{4}, \\ \frac{1}{2}(3x+y) – \frac{1}{2}(3x-y) = -\frac{1}{8} \] Solution Step 1: Simplify the Second Equation \[ \frac{1}{2}\big[(3x+y) – (3x-y)\big] = -\frac{1}{8} \] \[ \frac{1}{2}(2y) = -\frac{1}{8} \] \[ y = -\frac{1}{8} \quad […]

Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations: \[ \frac{10}{x+y} + \frac{2}{x-y} = 4, \\ \frac{15}{x+y} – \frac{9}{x-y} = -2 \] Solution Step 1: Make Suitable Substitution Let \[ \frac{1}{x+y} = a,\quad \frac{1}{x-y} = b \] Then the given equations become: \[ 10a + 2b

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

Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations: \[ \frac{44}{x+y} + \frac{30}{x-y} = 10, \\ \frac{55}{x+y} + \frac{40}{x-y} = 13 \] Solution Step 1: Make Suitable Substitution Let \[ \frac{1}{x+y} = a,\quad \frac{1}{x-y} = b \] Then the given equations become: \[ 44a + 30b

Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations: \[ 2(3u – v) = 5uv, \\ 2(u + 3v) = 5uv \] Solution Step 1: Simplify Both Equations First equation: \[ 2(3u – v) = 5uv \] \[ 6u – 2v = 5uv \quad \text{(1)} \]

Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations: \[ \frac{2}{3x+2y} + \frac{3}{3x-2y} = \frac{17}{5}, \\ \frac{5}{3x+2y} + \frac{1}{3x-2y} = 2 \] Solution Step 1: Make Suitable Substitution Let \[ \frac{1}{3x+2y} = a,\quad \frac{1}{3x-2y} = b \] Then the given equations become: \[ 2a + 3b

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}