Solve each of the following systems by using either addition or substitution. If a unique solution does not exist, state whether the system is dependent or inconsistent.
10x+2y=7
y=-5x+3
Any help is much appreciated...
2007-06-11 08:11:31 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Substitution Method
10x + 2y = 7-- - - - - -Equation 1
y = 5x + 3- - - - - - - - Equation 2
- - - - - - - - - - -
Substitute equation 2 into equation 1
10x + 2y = 7
10x + 2(- 5x + 3) = 7
10x + (- 10x + 6) = 7
10x - 10x + 6 = 7
No solution. The Coeficcient and variables cancell
- - - - - -s-
2007-06-11 08:22:31 · answer #1 · answered by SAMUEL D 7 · 0⤊ 0⤋
Substitution is quite straightforward. You were given an expression for y, which you can substitute into the first equation. That gives you 10x + 2(-5x + 3) = 7. That can be simplified to 10x - 10x + 6 = 7 ==> 6 = 7, an untrue statement. So this system is inconsistent. Had the system been independent, this procedure would have given you a simple equation in x which you could have solved algebraically, and then used the value for x in either equation to find y.
2007-06-11 15:16:18 · answer #2 · answered by DavidK93 7 · 0⤊ 0⤋
10x+2y=7 (1)
y=-5x+3 (2)
Substitute for y from (2) in (1):
10x + 2(3 - 5x) = 7
10x + 6 - 10x = 7
As this yields 6 = 7 and x disappears, the equations are inconsistent, and have no solution. Drawn on a graph, they are two parallel lines, as the first equation can be rewritten:
2y = 7 - 10x
y = 7/2 - 5x
showing that both lines have a gradient of -5.
2007-06-11 15:16:55 · answer #3 · answered by Anonymous · 0⤊ 0⤋
inconsistent. multiply second equation by 2 and get 10x+2y=6 so inconsistent
2007-06-11 15:17:14 · answer #4 · answered by terrell f 2 · 0⤊ 0⤋
10x+2y=7
y=-5x+3
2y= -10x +6
2y+10x = 6
solving the two
2y+10x=7
2y+10x=6
we dont get any solution
so its inconsistent
2007-06-11 15:15:39 · answer #5 · answered by sweet n simple 5 · 0⤊ 0⤋