Question 3050: My paper says i should solve this equation by substitution: 2x + 3y = 13
y = 3 - 2x
could you show me how to sleve this step by step
My paper also says solve this equation by elimination: 3x - y = 4
7x + 2y =18
could you also solve that step by step
Answer by thechamp1011(19)   (Show Source):
You can put this solution on YOUR website! 2x + 3y = 13
y = 3 - 2x
2x+3y=13
2x+y = 3
4x+4y =16
solve for X: 4x = 16-4y
x=16-4y/4 = 4-y=X????eq. 1
now solve for Y: y =3-[(2*(16-4x)/4]= 3 ? (8-2x)= -5+2x=Y??.eq. 2
Now plug Y in to the eq. 1: x=4-(-5+2x)=9-2x
3x=9, therefore X=3
Now plug X value in eq. 2: -5+2*3=Y
Y=1
3X-Y=4
7X+2Y=18
For PART 2, U CAN USE THE MATRIX ELIMINATION USING THE CROSS PRODUCT RULE.
SET UP MATRIX IN THE FOLLOWING FORMAT: [A] [T] = [C]
[A] [T] = [C]
3 -1 X 4
7 2 Y 18
FIND THE DETERMINANT OF [A]= (3*2)-(-1*7)=6+7=13
NOW FIND DETERMINANT OF X: (NOW U REWRITE THE [A] MATRIX AS FOLLOW:
[A]
4 -1
18 2
DETERMINANT OF x: (4*2)-(-1*18)=8+18=26
NOW FIND THE DETERMINAT OF Y: (NOW U REWRITE [A] MATRIX AS FOLLOW:
[A]
3 4
7 18
DETERMINANT OF y: (3*18)-(4*7)=26
NOW SOLVE FOR VARIABLE X: Dx/[A] = 26/13=2
THEREFORE, X=2
NOW SOLVE FOR VARIABLE Y: Dy/[A] = 26/13=2
THERFORE, Y=2
NOW CHECK IN THE ORIGINAL GIVEN EQUATION TO SEE IF THE ANSWER IS RIGHT :
3X-Y=4
(3*2)-2=4
4=4 , IT CHECKS
NOW CHECK THE SECOND EQUATION: 7X+2Y=18
(7*2)+(2*2)=18
14+4=18
18=18
ALSO CHECKCS...
THERFORE, X=2
AND Y=2
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