solve each system of equations using substitution. Show all work. write the solution as an ordered pair.
3x+y=4
6x+2y=7
heres another one:
x=0.5y+3
2x-y=6
graph the two lines
write both equations in slope-intercept form
2007-01-27 13:22:28 · 9 answers · asked by jenjen 3 in Science & Mathematics ➔ Mathematics
solve for one of the variables (x or y) and plug in what you get into the other equation. the easiest thing to do would be to solve for y in the first equation:
y= -3x + 4 (substracted 3x from both sides)
now you can plug in -3x+4 (which is equivalent to y) into the second equation for y.
6x + 2(-3x+4)=7
now distribute the 2 and you get:
6x + (-6x) + 8 = 7;
the 6x and -6x cancel, which leaves
8=7
this can never happen so the answer is NO SOLUTION. (the symbol for this is a zero with a diagnal slash through it.)
2nd question:
the first equation is already solved for x, so all you have to do is plug in that value into the second equation:
x = 0.5y + 3
2x - y = 6
2(0.5y + 3) - y = 6
distribute the 2:
(1)y+6 - y = 6
y and -y cancel out so that leaves:
6=6
6 is always going to equal 6 so your answer is: infinite number of solutions.
2007-01-27 13:39:34 · answer #1 · answered by π∑∞∫questionqueen 3 · 0⤊ 0⤋
With two unknowns you need two equations, which you have. *They must be unique too!
You solve one for one of the unknowns, then substitute it for the one you did not solve for.
Solve for y
3x+y=4
Subtract 3x from both sides.
y= -3x+4
Substitute -3x+4 every place you see y in the second equation.
6x+2y=7
6x+2(-3x+4) = 7
Now there is only one unknown, x
Clear the parentheses
6x-6x +8 = 7
Oops this is not a system if simultaneous equations! It has no answer!
The second set is not a simultaneous equation set either.
Bummer, I think they have misrepresented these questions.
2007-01-27 13:39:05 · answer #2 · answered by Ron H 6 · 0⤊ 0⤋
3x + y = 4
equals
y = 4 - 3x
6x + 2y = 7
equals
6x + 2(4 - 3x) = 7
equals
6x + 8 - 6x = 7
equals
8 = 7
I don't think so. No solution.
x = 0.5y + 3
equals
y = 2x - 6
2x - y = 6
equals
y = 2x - 6
Same line... Your teacher has issues.
2007-01-27 13:33:12 · answer #3 · answered by Bob 2 · 1⤊ 0⤋
usual form is Ax + by skill of = C the place A, B, and C are numbers. So x and y ought to be on a similar area. this implies #a million is already in usual form, different than you ought to make the A, B, and C into integers. the least puzzling way for that's to multiply by skill of 10... 10 (0.3x + 0.4y ) = (7.5) 10 3x + 4y = seventy 5 sturdy success at something!
2016-09-28 02:04:33 · answer #4 · answered by ? 4 · 0⤊ 0⤋
Buy a graphing calculator get the answer and work backwards da
2007-01-27 13:30:28 · answer #5 · answered by acupowderbill 1 · 0⤊ 0⤋
3x+y=4
6x+2y=7
y=4-3x
6x+2(4-3x)=7
Solve for x, then plug and chug for y.
Graphing is easy.
2007-01-27 13:26:38 · answer #6 · answered by sam_we_is 2 · 0⤊ 0⤋
3x+y=4
6x+2y=7
___________
(-2)3x+y=4
6x+2y=7
___________
-6x-2y=-8
6x+2y=7
___________
0=-1
___________
It's not a valid answer!
since i can't show you a graph on here good luck with the next one...
2007-01-27 13:34:08 · answer #7 · answered by nataliejluv008 2 · 0⤊ 0⤋
how can i graph just writing...and "pleez" letting other peeps do ur own hw(homework) is cheating!! so thats a "no" from me.
2007-01-27 13:28:02 · answer #8 · answered by Liz 3 · 1⤊ 0⤋
I would help you, I really would, but honey, you need to do your own work. Even if it is just a couple problems.
2007-01-27 13:27:10 · answer #9 · answered by Coalie 2 · 1⤊ 1⤋