Question

Question #0fad0

Answer 1

a) `(2/3, 10/3)`

b) `a = -36/11 = -3 3/11, b = 5/11`

Explanation:

a) For the first system of equations use elimination because you have a `+y` in the first equation and a `-y` in the second equation. Add the two equations directly:

`" "x + y = 4`
`"+ "2x - y = -2`

`" " 3x = 2; " "x = 2/3`

Substitute `x` back into one of the equations to find `y`:
`2/3 + y = 4/1*3/3`
`y = 12/3 - 2/3 = 10/3`

Solution a) `(2/3, 10/3)`

To check to see if this is correct, put this point into the second equation:
`2/1*2/3 - 10/3 = -6/3 = -2`

b) Rearrange the first equation to get `b = 2a + 7`
Substitute this equation into the second equation:
`-5a -3(2a + 7) = 15`

Distribute: `-5a -6a -21 = 15`

Add like-terms: `-11a -21 +21 = 15 + 21`

Simplify: `-11a = 36`

Divide by `-11: a = -36/11 = -3 3/11`

Substitute this value into `b = 2a + 7` to find `b`:
`b = 2*-36/11 + 7/1 * 11/11`
`b = -72/11 + 77/11 = 5/11`

Check the answer by inputting it into the second equation:
`-5/1*-36/11 - 3/1*5/11 = 180/11 - 15/11 = 165/11 = 15`