System Solutions

Question

The solution of the system 4x+5y=2 and 6x-2y=b is (3,a). Find the values of a and b

Answer 1

Replace x=3 and y=a to get new system as

12+5a=2

18-2a=b

So, a=-2 and b=22

Answer 2

From the point (3,a) we know x=3 We can plug this into the first equation to solve for y

4(3)+5y=2

12+5y=2 Subtract 12 from both sides

5y=-10 Divide both sides by -5

y=2 Therefor a=2

Next, take the y value and plug it into the second equation, you can solve for b

6(3)-2(-2)=b

18+4 = b

22=b

Answer 3

4x + 5y = 2

6x -2y = b

4(3) + 5y = 2

12 +5y = 2

5y = 2-12 = -10

y =-10/5 =-2

y =-2

a = y = -2

a=-2

solution is (3,-2) plug that in to solve for b

6(3) -2(-2) = b

b = 18+4 =22

b =22