SOLUTION: My son just does not understand this from the teacher's explanation. If you would please break down the steps to solve this one problem, hopefully we can apply the principals to t

Question 816184: My son just does not understand this from the teacher's explanation. If you would please break down the steps to solve this one problem, hopefully we can apply the principals to the other problems. Thank you very much.
2x + 3y = -1
3x + 4y = -4
Found 2 solutions by rothauserc, mananth:
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
2x + 3y = -1
3x + 4y = -4
This problem can be solved two ways
1) substitution
solve first equation for x
2x = -1 -3y
x = (-1 -3y) / 2
substitute for x in second equation
3*(-1 -3y)/2 +4y = -4
multiply both sides of = by 2
3*(-1 -3y) +8y = -8
-3 -9y +8y = -8
-y = -5
y = 5
solve for x in first equation
2x +3*(5) = -1
2x = -16
x = -8
check answers in second equation
3*-8 +4*5 = -4
-24 +20 = -4
-4 = -4
therefore
x = -8 and y = 5 is the correct solution
2) solve system of linear equations using matrices
2x + 3y = -1
3x + 4y = -4
first write the augmented matrix using the coefficients with the right column contains the constants
| 2 3 | -1 |
| 3 4 | -4 |
The objective is to reorganize the original matrix into one that looks like
| 1 0 | a |
| 0 1 | b |
where a and b are the solutions to the system
multiply row 2 by -1 and add to row 1
| -1 -1 | 3 |
| 3 4 | -4 |
multiply row 1 by 3 and add to row 2
| -1 -1 | 3 |
| 0 1 | 5 |
add row 2 to row 1
| -1 0 | 8 |
| 0 1 | 5 |
multiply row 1 by -1
| 1 0 | -8 |
| 0 1 | 5 |
This gives us the solution x = -8 and y = 5
Note that this matches with our substitution solution in 1) :-)

Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
2x + 3y = -1....................(1)
3x + 4y = -4.....................(2)
Practical approach to solving
we have to either eliminate x or y by adding the two equations
let us decide to eliminate x
so the coefficients of x should be same in both equations and their signs should be opposite
multiply (1) by -3
and (2) by 2
we get
-3(2x + 3y = -1)
2(3x + 4y = -4)

-6x-9y=3
6x+8y=-8
add the two equations
-6x & 6x cancel off
-9y+8y=-y
-y=-5
divide by -1
y=5
plug value of y in any equation
2x + 3y = -1
2x+3(5)=-1
2x+15=-1
2x=-16
/2
x=-8
x=-8, y=5
was it useful?
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