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I'm going to use the method of elimination to solve for x and y.
Multiply 1) by 3 and 2) by 2 to allow the x's to be eliminated.
1) 6x + 15y = 21
2) 6x + 12y = 6
Now subtract line 2 from line 1.
0x + 3y = 15
---- ----
3 3 divide both sides by 3 to get y by itself.
y =5.
Substitute into 1) to calculate x.
2x + 5(5) = 7
2x + 25 = 7
2x + 25 -25 = 7 - 25
2x = -18
---- ----- divide both sides by 2 to get x by itself
2 2
x = -9
Check by plugging in answer into the other equation, in this case 2)
3 (-9) + 6(5) = 3
-27 + 30 = 3
3 = 3
We did it correctly and checked to prove that we did it right.
(2x - 3y)(3x + 2y) = 2x*3x + 2x*2y - 3y*3x - 3y*2y = 6x^2 + 4xy - 9xy - 6y^2 = 6x^2 - 5xy - 6y^2
You multiply each element in the first set of brackets by each element in the second set of brackets and then consolidate like terms and arrange them in sequence of powers, first x and then y. So: 2x by 3x = 6x squared 2x by 2y = 4xy -3y by 3x = -9xy -3y by 2y = 6y squared
5x+3y=6 2x-4y=5 So 5x=6-3y so 2[(6-3y)/5]-4y=5 So x=(6-3y)/5 so 12-6y-20y=25 so -26y=25-12 so -26y=13 so y= -(1/2) 2x-4y=5 so 2x=5+4y so 2x=5+4(-1/2) so 2x=(10-4)/2 so 2x=6/4 so x =3/2
The value of x=3/2 and value of y= -1/2
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Hello,
You are talking of the distributivity of multiplication with respect to the addition or subtraction. The only term where you have multiplication and addition/subtraction is the one with parentheses because
4(5-6y) = 4*(5-6y). * means multiply by
Distributing the product consists in removing CORRECTLY the parentheses.
I consider the term alone
4*(5-6y) = 4*5 +4*(-6y)= 20 -4*6*y = 20 -24*y
You put this result in a package and replace it where it was it the original expression.
So
8*y -(package) +20= Replace package
8*y -(20-24*y)+20 = 8*y -20 -(-24y) + 20 Remember -*(-) = +
8*y -20 +24*y +20= Remember -20+20 =0
8*y -20 +20 +24*y= Addition is commutative
8*y +24*y = 32*y
Let y be an orange 8 oranges + 24 oranges =32 oranges.Coclusion 8y-4(5-8y)+20 = 32y
(1) if asking for graphing y= -2/3x+2, then press [diamond] [F1: Y=] type in .2/3x +2, see graph by [diamond][graph]
(2) if asking for graphing y= -2/3x+a, where a=3x, then first archive a=3x in Home screen by [home], type 3x [sto] a, then go back to y= menu, and type -2/3x+a in Y1
(3) if asking for graphing an equation that is dependent on 2 variables at the same time, use x-y-z axis (aka, change mode to graphing 3-D by [mode]graph [5:3D]) then enter desired equation in y= menu using Z function in terms of x and y aka z(x,y)= ...)
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