Question 63610: Can you please help me solve this system of equation using the substitution and elimination methods.
8x + 9 = -5y
-3x + 3y = -21
Found 3 solutions by stanbon, checkley71, Edwin McCravy:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1st: 8x + 9 = -5y
2nd: -3x + 3y = -21
---------
Divide thru 2nd by 3 to get:
-x+y=-7
Solve for y to get:
y=x-7
Substitute in 1st to get:
8x+9=-5(x-7)
8x+9=-5x+35
13x=26
x=2
---------
Substitute into y=x-7 to solve for y, as follows:
y=2-7=-5
Solution: (2,-5)
Cheers,
Stan H.
Answer by checkley71(8403) (Show Source):
You can put this solution on YOUR website! 8x+5y=-9
-3x+3y=-21 now multiply the first equatuion by 3 & multiply the second one by 8
24x+15y=-27
-24x+24y=-168 now add.
-----------------------------------
39y=-195
x=-195/39
x=-5 solution
3x+3*-5=-21
3x-15=-21
3x=6
x=6/3
x=2 solution
Answer by Edwin McCravy(20056)  (Show Source):
You can put this solution on YOUR website! Can you please help me solve this system of equation
using the substitution and elimination methods.
8x + 9 = -5y
-3x + 3y = -21
Rules for the substitution method:
1. Solve either equation for either letter. Call the letter you picked
the "first" letter.You'll get an expression, not a numerical value,
for the first letter. That expression will contain the other letter,
which we call the "second" letter.
2. Substitute the expression you get for the first letter in the OTHER
equation.
3. Solve for the value of the second letter. You'll get the actual value
for the second letter.
4. Substitute that value for the second letter in either equation.
5. Solve for the first letter. You'll get the value of the first letter.
8x + 9 = -5y
-3x + 3y = -21
1. Let's choose the bottom equation and choose the first letter as y.
We solve for y:
-3x + 3y = -21
+3x + 3x
-------------------
3y = -21 + 3x
Divide every term by the coefficient of y, which is 3:
3y/3 = -21/3 + 3x/3
y = -7 + x
2. Substitute the expression (-7 + x) for y in the top equation
8x + 9 = -5y
8x + 9 = -5(-7 + x)
3. Solve for x
8x + 9 = 35 - 5x
8x + 9 = 35 - 5x
-9 -9
---------------------
8x = 26 - 5x
+5x + 5x
-------------------------
13x = 26
Divide both sides by 13
13x/13 = 26/13
x = 2
4. Substitute x = 2 in either of the original
equations. I'll arbitrarily pick the first
one:
8x + 9 = -5y
8(2) + 9 = -5y
16 + 9 = -5y
25 = -5y
Divide both sides by -5
25/(-5) = -5y/(-5)
-5 = y
y = -5
So now we have the solution: (x, y) = (2, -5)
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Rule for the elimination method:
1. Choose a letter to eliminate, call it the "first" letter.
2. Arrange the equations so that the corresponding terms are
lined up vertically.
3. Find the LCM of the absolute values of the two coefficients
of the first letter.
4. Multiply each of the two equations respectively through by
whatever pair of numbers will cause the two coefficients to
have the same absolute value but opposite in sign.
5. Add term-by term vertically. You will get an equation in
only the second letter.
6. Solve for the second letter.
7. You have a choice here:
(a) Substitute the velue of the second letter in either
equation to find the value of the first letter
OR
(b) Start over with step 1 but this time choose the other
letter to eliminate.
8x + 9 = -5y
-3x + 3y = -21
1. Arbitrarily choose x to eliminate:
2. Line up the equations vertically like this:
8x + 5y = -9
-3x + 3y = -21
3. The LCM of 8 and 3 is 24.
4. Multiply the first equation through by 3 and
the second through by 8
3[ 8x + 5y = -9 ]
8[ -3x + 3y = -21 ]
24x + 15y = -27
-24x + 24y = -168
5. Add term-by term vertically:
24x + 15y = -27
-24x + 24y = -168
-----------------------
39y = -195
6. Solve for y:
39y = -195
Divide both sides by 39
y = -5
7. I'll choose to start over.
8x + 9 = -5y
-3x + 3y = -21
1. This time I choose y to eliminate:
2. Line up the equations vertically like this:
8x + 5y = -9
-3x + 3y = -21
3. The LCM of 5 and 3 is 15.
4. Multiply the first equation through by 3 and
the second through by -5
3[ 8x + 5y = -9 ]
-5[ -3x + 3y = -21 ]
24x + 15y = -27
15x - 15y = 105
5. Add term-by term vertically:
24x + 15y = -27
15x - 15y = 105
-----------------------
39x = 78
6. Solve for x:
39x = 78
Divide both sides by 39
y = 2
So now we have the solution: (x, y) = (2, -5)
Edwin
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