 Hello students, let's work out the following problem. It says solve the following system of equations by using the method of elimination by equating the coefficient. So let's now start the solution. The given system of equation is x by 10 plus y by 5 is equal to 14. x upon 8 plus y upon 6 is equal to 15. We'll first simplify this equation. The first one taking LCM we have LCM would be 10. So the first equation becomes x plus 2y upon 10 is equal to 14 and the second equation becomes 3x plus 4y upon 24. LCM of 6 and 8 would be 24. So dividing 24 by 8 we have 3 into x dividing 24 by 6 we have 4 into y that is 4y is equal to 15. Now the first equation becomes x plus 2y is equal to 14 into 10 that is 140 and the second equation becomes 3x plus 4y is equal to 15 into 24 that is 360. Let us name this as 1 and this as 2. Now we'll solve equation 1 and 2 by equating the coefficient and here we'll equate the coefficient of y. So to equate the coefficient of y we need to multiply equation 1 by 2 to make it 4. So multiply equation 1 by 2 and subtract. So multiplying equation 1 by 2 we have 2x plus 4y is equal to 140 into 2 is 280 and the second equation is 3x plus 4y is equal to 360. Now we have to subtract and we know that whenever we subtract sign changes. So 2x minus 3x is minus x plus 4y gets cancelled with minus 4y and 280 minus 360 is minus 80. So this implies x is equal to 80. Now to obtain the value of y we'll put x is equal to 80 in any one of the two equation 1 or 2. So here we'll put x is equal to 80 in equation 1. So we have equation 1 is x plus 2y is equal to 140. So 80 plus 2y is equal to 140. So this implies 2y is equal to 140 minus 80. So this implies 2y is equal to 140 minus 80 that is 60. This implies y is equal to 60 by 2 that is y is 30. Hence x is equal to 80 and y is equal to 30 is the required solution of given system of equation. So this completes the question and the session. Bye for now. Take care. Have a good day.