+19 Solve each of the following systems of equations. Find all solutions.
(a) \(\begin{align*} x+y&=-1,\\ 3x &= 4-3y. \end{align*}\)
(b)\(\begin{align*} 3x - 4y + 2&=0,\\ 10 - 10y& = 10y - 15x. \end{align*}\)
Thanks in advance!
+128475 a)
x + y = -1
3x = 4 - 3y
Rearrange the first equation as y = -1 - x
Sub this into the second equation for y
3x = 4 - 3(-1 - x) simplify
3x = 4 + 3 + 3x
3x = 7 + 3x dubtract 3x from both sides
0 = 7 this is absurd....so....this system has no solution
b)
3x - 4y + 2 = 0 ⇒ 3x - 4y = -2 (1)
10 - 10y = 10y - 15x
Divide the second equation through by 5 and we have
2 - 2y = 2y - 3x rearrange as
3x - 4y = -2 (2)
Notice that equations 1 and 2 are exactly the same.....so....when this happens....we have infinite solutions for both x and y
