It is yes for ordered pairs 1 and 4. It is no for ordered pairs 2 and 3.
Step-by-step explanation:
Step 1:
The given equations are multiples of each other so they have an infinite number of solutions.
So we need to substitute the values of x and y in the equations to determine which ordered pairs are solutions to the given equations.
Step 2:
When (x, y) = (7, 11), [tex]y =2x-3, 11 = 2(7)-3 = 14 -3 =11.[/tex]
[tex]6x-3y=9, 6(7) - 3(11) = 42 - 33 = 9.[/tex]
So the first ordered pair is a solution to the given system of equations.
When (x, y) = (4, -5), [tex]y =2x-3, -5= 2(4)-3 = 8 -3 =5.[/tex]
-5 ≠ 5,
So the second ordered pair is not a solution.
Step 3:
When (x, y) = (-1, 8), [tex]y=2x-3, 8 = 2(-1)-3 = -2-3 =-5.[/tex]
8 ≠ -5,
So the third ordered pair is not a solution.
When (x, y) = (0, -3), [tex]y =2x-3, -3 = 2(0)-3 = 0 -3 =-3.[/tex]
[tex]6x-3y=9, 6(0) - 3(-3) = 0 + 9 = 9.[/tex]
So the fourth ordered pair is a solution to the given system of equations.
