what is the best method to solve the system of equation??
2007-01-18 13:29:21 · 5 answers · asked by gayle325 1 in Science & Mathematics ➔ Mathematics
Solve for one variable in terms of the other in one equation, and then substitute this solution in the other equation:
2x +2y = 8
x + y = 4
y = 4 - x
Now substitute y = 4 - x in 5x - 2y = 4 and solve for x:
5x -2y = 5x - 2 (4 - x) = 5x -8 + 2x = 4
7x - 8 = 4
7x = 12
x = 12/7 = 1.714
substitute x = 12/7 in 2x + 2y = 8 and solve for y:
2 (12/7) + 2y = 8
24/7 + 2y = 8
12/7 + y = 4
y = 4 - 12/7 = 28/7 - 12/7 = 16/7 = 2.286
check by substitution in 5x - 2y = 4:
5 (12/7) - 2 (16/7) = 4
60/7 - 32/7 = 28/7 = 4
check by substitution in 2x + 2y = 8:
2 (12/7) + 2 (16/7) = 24/7 + 32/7 = 56/7 = 8
2007-01-18 14:00:12 · answer #1 · answered by hevans1944 5 · 0⤊ 0⤋
First, add equals to equals.
On the left you have 5x - 2y +2x + 2y and on the right you have 8 + 4. Simplifying,
7x = 12
x = 12/7 or 1 5/7
Then you take either equation and substitute 12/7 for x and see what y is. Taking the first
5(12/7) - 2y = 4
60/7 -2y = 4
transposing and changing 4 to 28/7 you get
60/7 - 28/7 = 2y
32/7 = 2y
16/7 = y
Then substitute for x and y in the other equation to make sure you didn't make a mistake.
2(12/7) + 2(16/7) =? 8
24/7 + 32/7
56/7 = 8
2007-01-18 21:42:45 · answer #2 · answered by Tracey T 2 · 0⤊ 0⤋
Solve equation 5x-2y=4
Subtract 5x from both sides and get
-2y=4-5x
Divide -2 from both sides
y= 4/-2 - 5x/-2
y= -2 + 2 1/2x
y= 1/2x
Solve for x:
5x-2(1/2x)=4
5x-2/2x
5x- 1x =4
4x =4
Divide both sides by 4 & get
x=1
Solve for y: y=1/2x y=12(1) y=1/2
Check equation: 5x-2y=4
5(1) - 2(1/2) = 4
5 - 2/2 =4
5 - 1 =4
4 = 4
2007-01-18 22:36:16 · answer #3 · answered by Angel B 1 · 0⤊ 1⤋
Addition method, because by adding the equations as they are, the y variable will be eliminated, allowing us to solve for x..
5x -2y = 4 Eq1
2x +2y = 8 Eq2
Add Eq1 + Eq2
7x + 0y = 12
x = 12/7 = 1.714
Sub x=12/7 into second equation
2(12/7) + 2y = 8
2y = 8-24/7
y = 2.285
Check
5x-2y = 4
5(1.714) - 2(2.285) = 4
8.57 - 4.57 = 4
4 = 4
2007-01-18 21:36:38 · answer #4 · answered by Wolfshadow 3 · 1⤊ 0⤋
start with the first problem and solve for either x or y. If you solve for x, then take the equation that it equals, plug it in for x in the second equation and solve for y. Then take that answer and plug it in for y in either original equation and solve for x.
2007-01-18 21:39:10 · answer #5 · answered by je t'♥ 5 · 0⤊ 0⤋