3x-2y=11
x+y=7
2006-12-04 09:19:01 · 8 answers · asked by Elsa R 1 in Science & Mathematics ➔ Mathematics
x + y = 7 (subtract x from both sides)
y = 7 - x
3x - 2y = 11 (substitute in for y)
3x - 2(7 - x) = 11
3x - 14 + 2x = 11
5x = 25
x = 5
y = 7 - x
y = 7 - 5
y = 2
answer: (5, 2)
check: 3x - 2y = 11
3(5) - 2(2) = 11
15 - 4 = 11
2006-12-04 09:23:44 · answer #1 · answered by babylobuhster 2 · 1⤊ 0⤋
You can solve one of three ways: Substitution, Elimination, or Matrices. For simple equations like this, substitution and elimination are easier than matrices, so I'll explain each of these.
SUBSTITUTION--For subtstitution, you will set one variable equal to an expression involving only the other variable so you can plug this into the other equation and solve.
3x-2y=11
x+y=7
The second seems easier, so you can pick which variable you want to solve for from the second one. I'll pick x, so...
3x-2y=11 and
x=-y+7
Since we know that x is the same as (-y+7), we can replace x with (-y+7) in the first equation, so...
3(-y+7)-2y=11. Now you only have one variable and you can solve.
-3y+21-2y=11 --> -5y=-10 --> y=2 Now plug in 2 for y in the second equation. x+2=7 --> x=5
ELIMINATION-In this method, you will eliminate one variable by multiplying one equation by a number so it cancels with the other.
3x-2y=11
x+y=7 Let's eliminate the x. Because we're adding the equations and getting rid of x, we will multiply everything in the second equation by -3 so we have 3x-2y=11 and -3x-3y=-21. Add the x terms, the y terms, and the constants to form one new equation. -3x+3x=0 -3y-2y=-5y -21+11=-10 New equation is...
-5y=-10 --> y=2
Plug back in:
x+2=7
x=5
Hope this helps!
2006-12-04 17:38:53 · answer #2 · answered by Pius Thicknesse 4 · 1⤊ 0⤋
3x - 2y = 11
x + y = 7
Your first step is to subtract the equations in such a fashion that one of the variables gets eliminated. Let's multiply the second equation by 3, in order to have it match up with the other equation which has 3x.
3x - 2y = 11
3x + 3y = 21
Now, sutract the two equations from each other, to get
(3x - 2y) - (3x + 3y) = 11 - 21
-5y = -10
y = 2
Since you have y = 2, you can now plug in 2 into one of the equations to get x. Let's use the second one, because it's simpler.
x+y=7
x+2= 7
x = 5
Therefore, x = 5 and y = 2.
2006-12-04 17:22:03 · answer #3 · answered by Puggy 7 · 1⤊ 0⤋
Multiply the second equation by 2 to obtain 2x+2y=14. Add this equation to the first equation to get (3x+2x) + (2y-2y) = 25 which simplifies to 5x=25 or x=5. Plug x=5 into either equation to get y=2.
Paul
2006-12-04 17:23:26 · answer #4 · answered by Paul 1 · 1⤊ 0⤋
3x-2y=11
x+y=7 multiply ny 2
2x+2y=14
3x-2y=11 add
5x=25 divide by 5
x=5
substitute
x+y=7
5+y=7 subtract 5
y=2
solution is (5,2)
check
3*5-2*2=11
15-4=11
11=11
2006-12-04 17:37:30 · answer #5 · answered by yupchagee 7 · 1⤊ 0⤋
Rearranging the equations:
y=7-x
3x-2(7+x)=11
3x-14+2x=11
5x+14=11
5x=25
x=5
y=7-x
y=7-5
y=2
2006-12-04 17:23:47 · answer #6 · answered by dixiechck615 3 · 0⤊ 0⤋
Use linear combination, that means that yu multiply one or both equations by a scale factor (a diff one for each equation) and add them so as to cancel one of the variables.
In your case, multiply the bottom one by 2 and add them.
you get: 5x=25
x=5
and then substitute that into one of the original equations and solve for the other variable.
5+y=7
y=2
solution = (5,2)
2006-12-04 17:23:04 · answer #7 · answered by Scooter_MacGyver 3 · 0⤊ 0⤋
y= 1.5x+ 5.5
y= -x-7
2006-12-04 17:23:17 · answer #8 · answered by Anonymous · 0⤊ 0⤋