SOLUTION: solve the following systems using the elimination method. Write your complete solutions. 1. x - 2y = 5 and 2x + 3y = -32 2. 3x + 4y = 3 and 2x - 3y = 19 3. 3x + 5y = -14 a

Algebra ->  Linear-equations -> SOLUTION: solve the following systems using the elimination method. Write your complete solutions. 1. x - 2y = 5 and 2x + 3y = -32 2. 3x + 4y = 3 and 2x - 3y = 19 3. 3x + 5y = -14 a      Log On


   

Question 1199023: solve the following systems using the elimination method. Write your complete solutions.
1. x - 2y = 5 and 2x + 3y = -32
2. 3x + 4y = 3 and 2x - 3y = 19
3. 3x + 5y = -14 and 2x - y = -18
Found 2 solutions by math_tutor2020, josgarithmetic:
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

The rule on this website is that you need to post one problem at a time (or one problem per post).
I'll do problem 1 to get you started.

The system we have is
system%28x-2y=5%2C2x%2B3y=-32%29
If we were to add the equations straight down, then:
x+2x = 3x
-2y+3y = 1y = y
None of the variables cancel.
Same goes if we were to subtract the equations.

What we need is to have the coefficients of either x or y match up so they cancel.

Let's say we doubled everything in the 1st equation
We'd go from x-2y = 5 to 2x-4y = 10

Now we have this updated equivalent system
system%282x-4y=10%2C2x%2B3y=-32%29
We can subtract the equations straight down
2x-2x = 0x = 0, the x terms go away
-4x-3y = -7y
10-(-32) = 10+32 = 42

We end up with the equation -7y = 42 which solves to y = -6.

Then use that y value to find x.
Pick either equation with x and y.
Let's say we chose the 1st equation.
x - 2y = 5
x - 2(-6) = 5
x + 12 = 5
x = 5-12
x = -7
Or you can pick on the 2nd equation.
2x+3y = -32
2x+3(-6) = -32
2x-18 = -32
2x = -32+18
2x = -14
x = -14/2
x = -7
Either way you should get the same x value.
This helps confirm you have the correct solution.

A visual way to confirm the answer is to graph each equation onto the same xy grid.
I recommend either Desmos or GeoGebra as two graphing options.

x - 2y = 5 in green and 2x + 3y = -32 in blue
The two lines intersect at (-7, -6)

Or you could plug each coordinate of (-7,-6) back into the original equations.
You should get true results after simplifying everything.

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Answer: (x,y) = (-7, -6)

Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
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2. 3x + 4y = 3 and 2x - 3y = 19
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Multiply E1 by 2 and E2 by 3; and eliminate the x to find y.

Multiply E1 by 3 and E2 by 4; and eliminate the y to find x.