🌟 [ 14 ]   How solve linear equations with two variable||Class 10 maths||CBSE Board Exams [ @Mathematics Solution ]

#How solve linear equations with two variables #linearequations in two variables examples #linearequations in two variables examples calculator #linearequations in two variables examples Class 10 #linearequations in two variables examples worksheet Linear equation in two variables SUMMARY A system of two linear equations in x and y has (i)a unique solution if the graph lines intersect at a point (ii) infinitely many solutions if the two graph lines coincide (iii)no solution if the two graph lines are parallel (I)Substitution method Step 1. Express y in terms of x in one of the given equations. Step 2. Substitute this value of y in terms of x in the other equation. This gives a linear equation in x. Step 3. Solve the linear equation in x obtained in Step 2. Step 4. Substitute this value of x in the relation taken in Step 1 to obtain a linear equation in y. Step 5. Solve the above linear equation in y to get the value of y. (II) ELIMINATION METHOD METHOD In this method, we eliminate one of the unknown variables and proceed using the following steps. Step 1. Multiply the given equations by suitable numbers so as to make the coefficients of one of the unknown variables numerically equal. Step 2. If the numerically equal coefficients are opposite in sign then add the new equations. Otherwise, subtract them. Step 3. The resulting equation is linear in one unknown variable. Solve it to get the value of one of the unknown quantities. Step 4. Substitute this value in any of the given equations. Step 5. Solve it to get the value of the other unknown variable. 1. Solve graphically the system of linear equations: 4x – 5y = -16 and 2x + y = 6. Determine the vertices of the triangle formed by these lines and the x-axis. Find the coordinates of the points where the graph lines cut the y-axis. [CBSE 2002C] [CBSE 2006] 2. Solve for x and y: 0.4 x – 1.5 y = 6.5 and 0.3 x + 0.2 y = 0.9 [CBSE 2000, ‘04C, ‘05] 3. Solve for x and y: 4/x + 3y = 8 and 6/x 4y =5[CB .

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