5x - 3y= 14
2x - y =6
2006-12-20 10:32:54 · 8 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
multiply (2) by -3
-6x+3y=-18
5x-3y=14
adding
-x=-4
x=4
substituting
20-3y=14
adding -20
-3y=-6
dividing by -3
y=2
check
20-6=14 checks
8-2=6 checks
2006-12-20 10:39:04 · answer #1 · answered by raj 7 · 3⤊ 0⤋
Addition method .. multiply second equation by -3, this is the easiest way to get rid of a variable, easier than getting rid of the x which involves two multiplications rather than just one. So you have
5x - 3y = 14
-6x + 3y = -18
add them and you get -x = -4 so x = 4
Put this back into the easier equation and find y
2(4) - y = 6
8 - y = 6
y = 2
Finally, put both numbers back into the other equation and make sure they work
5(4) - 3(2) = 14 20 - 6 = 14 ok
2006-12-20 18:47:08 · answer #2 · answered by Joni DaNerd 6 · 3⤊ 0⤋
5x - 3y= 14
2x - y =6 multiply both sides by -3
-6x+3y=-18
5x - 3y= 14 add
-x=-4 divide by -1
x=4
2x - y =6 substitute
2*4-y=6 subtract 8 from each side
-y=-2 multiply by -1
y=2 solution is (4, 2)
check
5x - 3y= 14
5*4-3*2=14
20-6=14
14=14
2006-12-20 18:50:45 · answer #3 · answered by yupchagee 7 · 3⤊ 0⤋
First, multiply the 2nd equation by -3 to cancel the y's
You get -6x +3 y = -18
Add this with the first equation
-x = -4
x = 4
Substitute x = 4 in either equation to get y
In the 2nd equation:
8 - y = 6
y = 2
In the 1st equation:
20 - 3y = 14
-3y = -6
y = 2
Both answers being the same confirms the calculations were correct
2006-12-21 00:33:03 · answer #4 · answered by Renaud 3 · 2⤊ 0⤋
Multiply the second equation by -3:
5x-3y=14
-6x+3y=-18
=========
-x=-4
x=4
5(4)-3y=14
20-3y=14
-3y=-6
y=2
(4,2)
Check:
5(4)-3(2)=14
20-6=14
14=14
2(4)-2=6
8-2=6
6=6
2006-12-20 22:54:37 · answer #5 · answered by Anonymous · 2⤊ 0⤋
1) 5x - 3y = 14
2) 2x - y = 6
In order to do addition we must first manipulate one of the equations so the coefficients of one of the variables have the same absolute value with opposite signs.
Multiply equation 2 by - 3
2a) -6x + 3y = - 18
1) 5x - 3y = 14
- - - - - - - - - - - - -
- x = - 4
x = 4
Substitute this into equation 1
5(4) - 3y = 14
20 - 3y = 14
-3y = - 6
y = 2
Check using equation 2
2x - y = 6
2(4) - 2 = 6
6 = 6
2006-12-20 18:42:35 · answer #6 · answered by kindricko 7 · 3⤊ 0⤋
*Solve for "x" or "y" by eliminating a variable: Let's eliminate "y"
First: take the second coefficient (-3) from the first equation and multiply it by the second equation. Take the second coefficient (-1) from the second equation and multiply it by the first equation. Both coefficients are negative, make one positive to eliminate "y" so, let's make 1 positive.
1(5x - 3y = 14)
-3(2x - 1y = 6)
--------------------
5x - 3y = 14
+ -6x + 3y = -18
--------------------
-x = - 4 change to x = 4
Second: take the first coefficient (5) from the first equation and multiply it by the second equation. Take the second coefficient (2) from the second equation and multiply it by the first equation. Both coefficients are positive, make one negative to eliminate "x" so, let's make 2 negative.
-2(5x - 3y = 14)
5(2x - 1y = 6)
--------------------
-10x + 6y = -28
+ 10x - 5y = 30
--------------------
y = 2
2006-12-21 01:36:28 · answer #7 · answered by ♪♥Annie♥♪ 6 · 1⤊ 0⤋
-6x + 3y = -18
-x = -4
x = 4
8 - y = 6
y = 2
x = 4, y = 2
2006-12-20 18:41:24 · answer #8 · answered by novadeath69 2 · 3⤊ 0⤋