Solve the system of equations using the substitution method.
If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is “no solution” or “infinitely many solutions.”
-4x + y = 8
2x + 3y = -1
2006-12-24 14:52:10 · 2 answers · asked by ? 1 in Education & Reference ➔ Homework Help
From the first equation, y = 8 + 4x. Now substitute 8+4x for y in the second equation, and you get
2x + 3(8+4x) = -1
which simplifies to
14x = -25
so x = -25/14. Substitute this back into y = 8 + 4x to get y = 8 + 4(-25/14) = 8 -100/14 = 5/7.
This is the unique solution, which, written as an ordered pair, is
(-25/14,5/7)
2006-12-24 15:09:44 · answer #1 · answered by James L 5 · 0⤊ 0⤋
multiply second equation ( 2x+3y=-1) by -2
-4x-6y=2
-4x=2+6y------------ put in first equation
2+6y+y=8
7y+2=8
7y=6
y=6/7put in any equation to get the value of x
2x+3(6/7)=-1
2x=(-18/7)-1
x=-25/14
The equations have unique solution (-25/14,6/7)
2006-12-24 23:22:29 · answer #2 · answered by chumbawamba 1 · 0⤊ 0⤋