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
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: \[ bx + cy = a + b, \] \[ ax\left(\frac{1}{a-b}-\frac{1}{a+b}\right) + cy\left(\frac{1}{b-a}-\frac{1}{b+a}\right) = \frac{2a}{a+b} \] Solution Step 1: Simplify the Second Equation \[ \frac{1}{a-b}-\frac{1}{a+b} = \frac{(a+b)-(a-b)}{a^2-b^2} = \frac{2b}{a^2-b^2} \] \[
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: \[ x\left(a-b+\frac{ab}{a-b}\right) = y\left(a+b-\frac{ab}{a-b}\right), \\ x + y = 2a^2 \] Solution Step 1: Simplify the Coefficients \[ a-b+\frac{ab}{a-b} = \frac{(a-b)^2 + ab}{a-b} = \frac{a^2 – ab + b^2}{a-b} \] \[
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: \[ (a+2b)x + (2a-b)y = 2 \\ , (a-2b)x + (2a+b)y = 3 \] 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: \[ 5ax + 6by = 28 \\ , 3ax + 4by = 18 \] Solution Step 1: Reduce the Equations Let \[ X = ax,\quad Y = by \] Then the
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: \[ 2ax + 3by = a + 2b \\ , 3ax + 2by = 2a + b \] Solution Step 1: Compare with the Standard Form The standard form is: \[
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: \[ \frac{x}{a} = \frac{y}{b}, \\ ax + by = a^2 + b^2 \] Solution Step 1: Convert the First Equation into Linear Form From \[ \frac{x}{a} = \frac{y}{b} \] cross-multiplying, we
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: \[ \frac{x}{a} + \frac{y}{b} = a + b,\quad \frac{x}{a^2} + \frac{y}{b^2} = 2 \] Solution Step 1: Substitute Variables Let \[ \frac{x}{a} = u,\quad \frac{y}{b} = v \] Then the given
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: \[ \frac{x}{a} + \frac{y}{b} = 2, \\ ax – by = a^2 – b^2 \] Solution Step 1: Reduce to Linear Equations Multiply the first equation by \(ab\): \[ bx +
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: \[ \frac{57}{x+y} + \frac{6}{x-y} = 5,\quad \frac{38}{x+y} + \frac{21}{x-y} = 9 \] Solution Step 1: Substitute Variables Let \[ \frac{1}{x+y} = u,\quad \frac{1}{x-y} = v \] Then the given equations become: