Solve the system using the linear combination method. Please show work.?

Question

2x -7y = -10
3x +2y= 10

Answer 1

2x -7y = -10
3x +2y= 10

Multiply the first equation by 3 and the second by 2
6x - 21y = -30
6x + 4y = 20

Subtract the second equation from the first
0x -25y = -50
y = -50 / -25 = 2

Plug your result for y back into the first equation and solve for x:

2x -(7)(2) = -10
2x -14 = 10
2x = 4
x = 2

Check these results in the second equation to validate:
(3)(2) + (2)(2) ?= 10
6 + 4 ?= 10
10 = 10

Your answer is thus x=2, y=2

Answer 2

The linear combination method pretty much means make one of the variables in each equation equal and opposite in sign of the other equation. The first way that pops in to my head is to get each equation to have a 14y, one negative and one positive. We do this by:

2(2x -7y = -10)
7(3x +2y= 10)

this gives us

4x - 14y = -20
21x + 14y = 70

Now we can add these equations using the "linear combination method"

4x - 14y = -20
21x + 14y = 70
+__________________
25x + 0 = 50

This is easily simplified by dividing everyting by 25

Yielding

x = 2 , NOW we are only HALF done. We must substitute our x back into one of the original equations to find out what y is.

substituting x = 2 in:
3(2) +2y= 10
6 + 2y = 10 now solving for y

y = 4/2
y = 2

Plugging these back in to check in one of our original equations holds true. This is the linear combination method.

Answer 3

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Solve the system using the linear combination method. Please show work.?
2x -7y = -10
3x +2y= 10

Answer 4

let, 2x-3y = 4 be equation -1 and let, 8x +3y = 1 be equation -2. taking eq 1 -> 2x = 4 +3y -> x = 4+3y/2 (equation 3) now taking eq 2 and substituting the value of x in eq 3 -> i.e., -> 8(4+3y/2) + 3y = 1 32 + 24y /2 +3y = 1 32 +24 y + 6y /2 = 1(taking l.c.m) 32 + 30y = 2(by cross multiplication) 30y = 32 - 2 30 y = 30 y = 30/30 y = 1 (equation 4) now, putting the value of y of eq - 4 in eq - 3) x = 4+3y/2 x = 4 + (3*1)/2 x = 4+3/2 x = 7/2 Therefore, x = 7/2 & y = 1 -> ans

Answer 5

2x -7y = -10 <-- Eq 1
3x +2y= 10 <-- Eq 2
4x -14y = -20 <-- Eq3 = 2*Eq 1
21x +14y =70 <-- Eq4 = 7*EQ 2
25x =50 <-- Eq2 + Eq 4
x = 2
3(2) +2y = 10 <-- Put x = 2 in Eq 2
2y=4
y=2