SOLUTION: Solve the equations using elimination and substitution (1)2x+3y=11 4x+y=12 (2)3x+2y=24 2x-3y=42

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Question 1134703: Solve the equations using elimination and substitution
(1)2x+3y=11
4x+y=12
(2)3x+2y=24
2x-3y=42

Found 2 solutions by Boreal, MathLover1:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
First by substitution
y=-4x+12
substitute into the top to get 2x+3(-4x+12)=11
2x-12x+36=11
-10x=-25
x=2.5
substitute into second and y=2
check in top one and 2(2.5)+3(2) does =11
(2.5, 2)
Do by elimination
multiply top by -2
-4x-6y=-22
4x+y=12
-5y=-10
y=2
x=2.5
Do the second by elimination
Multiply the top by 3 and the bottom by 2, which will make 6y and -6y which cancel each other
9x+6y=72
4x-6y=84
13x=156
x=12
y=-6
(12, -6), and that checks
One can do substitution but more difficult here. x=(-2/3)y+8 or y=(-3/2)x+12 and put into the second equation.

Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

(1)
.....eq.1
......eq.2
------------------------
start with
......eq.2...solve for
.......eq.2a...substitute in eq.1 to eliminate variable


.....eq.1
...solve for





go back to eq.2a, substitute for




solution is intersection point (,)=(,)
(2)
.......eq.1
.......eq.2
---------------------------
start with
.......eq.1 ..solve for


...........eq.1a
go to
.......eq.2...substitute in from eq.1a to eliminate variable


.........both sides multiply by




go back to eq.1a
...........eq.1a substitute for and solve for






solution is intersection point (,)=(,)

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