SOLUTION: solve using addition method 3x+7y=16 2x-3y=-11

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Question 999141: solve using addition method
3x+7y=16
2x-3y=-11
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52794) (Show Source):
You can put this solution on YOUR website!
.
3x + 7y = 16 (1) 2x - 3y = -11 (2) Multiply (1) by 3 (both sides) and (2) by 7 (both sides). 9x + 21y = 48 (1') 14x -21y = -77 (2') Now add (1') and (2'). In this way you will exclude y and will obtain a single equation for x: 9x + 14x = 48 - 77, or 23x = -29. Hence, x = . Now substitute this value of x into the equation (1) and solve it for y. The numbers are really not very impressive, but they are your numbers, not my.

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
your equations are:

3x+7y=16
2x-3y=-11

multiply both sides of the first equation by 2 and multiply both sides of the second equation by 3 to get:

6x + 14y = 32
6x - 9y = -33

subtract the second equation from the first to get:

23y = 65

solve for y to get y = 65/23

replace y with 65/23 in the original first equation to get:

3x+7y=16 becomes:
3x + 7*65/23 = 16

simplify to get:

3x + 455/23 = 16

multiply both sides of this equation by 23 to get:

69x + 455 = 368

subtract 455 from both sides of this equation to get:

69x = 368 - 455

simplify to get:

69x = -87

divide both sides of this equation by 69 to get:

x = -87/69

you have:

x = -87/69
y = 65/23

to confirm these solutions are correct, replace x and y in the original equations to get:

3x+7y=16
2x-3y=-11

become:

3*-87/69 + 7*65/23 = 16
2*-87/69 - 3*65/23 = -11

evaluate both equations using your calculator (unless you want to punish yourself by doing the math manually) to get:

16 = 16
-11 = -11

the solutions are confirmed as good.

x = -87/69
y = 65/23

x = -87/69 can be simplified to x = -29/23
y = 65/23 remains at y = 65/23 since it cannot be simplified any further.