Consistency of a Pair of Linear Equations Video Explanation Question Determine whether the following system of equations has a unique solution, no solution or infinitely many solutions. If it has a unique solution, find it: \[ x – 3y = 3, \qquad 3x – 9y = 2 \] Solution Step 1: Write in Standard Form […]
Solve the System of Equations by the Method of Cross-Multiplication Video Explanation Question Solve the following system of equations by the method of cross-multiplication: \[ \frac{b}{a}x + \frac{a}{b}y = a^2 + b^2, \\ x + y = 2ab \] Solution Step 1: Convert the First Equation into Linear Form Multiply the first equation by \(ab\):
Solve the System of Equations by the Method of Cross-Multiplication Video Explanation Question Solve the following system of equations by the method of cross-multiplication: \[ \frac{ax}{b} – \frac{by}{a} = a + b, \\ ax – by = 2ab \] Solution Step 1: Convert the First Equation into Linear Form Multiply the first equation by \(ab\):
Solve the System of Equations by the Method of Cross-Multiplication Video Explanation Question Solve the following system of equations by the method of cross-multiplication: \[ mx – ny = m^2 + n^2 \\ x + y = 2m \] Solution Step 1: Compare with the Standard Form \[ a_1x + b_1y = c_1,\quad a_2x +
Solve the System of Equations by the Method of Cross-Multiplication Video Explanation Question Solve the following system of equations by the method of cross-multiplication (where \(x \neq 0\) and \(y \neq 0\)): \[ \frac{a^2}{x} – \frac{b^2}{y} = 0, \\ \frac{a^2 b}{x} + \frac{b^2 a}{y} = a + b \] Solution Step 1: Convert into Linear
Solve the System of Equations by the Method of Cross-Multiplication Video Explanation Question Solve the following system of equations by the method of cross-multiplication: \[ 6(ax + by) = 3a + 2b \\ , 6(bx – ay) = 3b – 2a \] Solution Step 1: Simplify the Given Equations \[ ax + by = \frac{3a
Solve the System of Equations by the Method of Cross-Multiplication Video Explanation Question Solve the following system of equations by the method of cross-multiplication: \[ 2(ax – by) + a + 4b = 0 \\ , 2(bx + ay) + b – 4a = 0 \] Solution Step 1: Simplify the Given Equations First equation:
Solve the System of Equations by the Method of Cross-Multiplication Video Explanation Question Solve the following system of equations by the method of cross-multiplication: \[ ax + by = \frac{a+b}{2} \\ , 3x + 5y = 4 \] Solution Step 1: Compare with the Standard Form The standard form is: \[ a_1x + b_1y =
Solve the System of Equations by the Method of Cross-Multiplication Video Explanation Question Solve the following system of equations by the method of cross-multiplication: \[ a^2x + b^2y = c^2 \\ , b^2x + a^2y = a^2 \] Solution Step 1: Compare with the Standard Form The standard form is: \[ a_1x + b_1y =
Solve the System of Equations by the Method of Cross-Multiplication Video Explanation Question Solve the following system of equations by the method of cross-multiplication: \[ (a-b)x + (a+b)y = 2a^2 – 2b^2, \] \[ (a+b)(x+y) = 4ab \] Solution Step 1: Write the Equations in Standard Form First equation: \[ (a-b)x + (a+b)y = 2(a^2