MATH SOLVE

4 months ago

Q:
# consider the following system with a solution (1,3) equation 1 of the system 2x+y=5 equation 2 of the system x-2y=-5 prove that replacing the first equation with the sum of the equation and a multiple of the other produces a system with the same solution

Accepted Solution

A:

Answer:The prove in the procedureStep-by-step explanation:we have2x+y=5 -----> equation 1x-2y=-5 ----> equation 2soReplace the first equation with the sum of the equation and a multiple of the otherMultiply equation 2 by 3 both sides3*(x-2y)=-5*33x-6y=-15 ----> equation 3Adds equation 3 and equation 13x-6y=-152x+y=5 --------------3x+2x-6y+y=-15+55x-5y=-10 -----> equation 4The new system is5x-5y=-10 -----> equation 4x-2y=-5 ----> equation 2Solve the system by eliminationMultiply equation 2 by -5 both sides-5*(x-2y)=-5*(-5)-5x+10y=25 -----> equation 5Adds equation 4 and equation 55x-5y=-10 -5x+10y=25------------------5y+10y=-10+255y=15y=3Find the value of xsubstitute the value of y in the equation 2x-2y=-5 x-2(3)=-5x-6=-5x=-5+6x=1The solution of the new system of equations is (1,3)thereforeThe solution of the new system of equations is the same solution of the original system of equations.