Q:

Consider the following system of equations. x+y=11 and 2x - 3y=-3. Which equation can be added to the system so that the solution does not change.A) x-y=2B) -2x+2y=-2C)3x+y=20D)x+2y=18​

Accepted Solution

A:
Answer:B) -2x+2y=-2Step-by-step explanation:we have[tex]x+y=11[/tex] ----> equation A[tex]2x-3y=-3[/tex] ----> equation BSolve the system by graphingRemember that the solution of the system of equations is the intersection point both graphsusing a graphing toolThe solution is the point (6,5)see the attached figureRemember thatIf a equation is added to the system so that the solution does not change, then the solution of the system must be a solution of the equation added Verify each caseThe solution of the system is (6,5)substitute the value of x and the value of y in each equationcase A) x-y=2 6-5=21=2 ----> is not truethereforeThis equation can't be added to the systemcase B) -2x+2y=-2-2(6)+2(5)=-2-12+10=-2-2=-2 ----> is truethereforeThis equation can be added to the systemcase C) 3x+y=203(6)+5=2018+5=2023=20 ----> is not truethereforeThis equation can't be added to the systemcase D) x+2y=18​5+2(6)=185+12=1817=18 ----> is not truethereforeThis equation can't be added to the system