Question

For what ordered pair (a,b) are there infinite solutions (x,y) to the system ; 3ax + 3y=5b, 2x+y=5

Answer 1

(2,3)

Explanation:

For there to be infinite solutions, the first equation needs to be consistent with the second and yet add no new information, which means it must be a multiple of the second. Since the coefficient of y in the first equation is three times that of y in the second equation, the multiplier is 3. This implies that the first equation must be 3(2x+y)=3(5). After equating coefficients, this gives 3a=3×2 and $5b=3×5, or (a,b)=(2,3).

Answer 2

The ordered pair is (2,3)

Explanation:

we know that

If a system of equations has infinite solutions, then the equations are the same

we have

3ax+3y=5b -----> equation A

2x+y=5 ----> equation B

Multiply equation B by 3 both sides

3*(2x+y)=5*3

6x+3y=15 -----> equation C

Compare equation A and equation C

so

3ax=6x------> 3a=6 -----> a=2

5b=15 ------> b=3

The ordered pair is (2,3)