one more question?

Question

3a + 4b = -25

2a - 3b = 6


and...

y = x + 2

2x + y = 11



i am so stuck please and thanks

Answer 1

3a + 4b = -25
2a - 3b = 6

(3a + 4b = -25) x 3
(2a - 3b = 6) x 4

9a +12b = -75 ----------> equation 1
8a - 12b = 24 -----------> equation 2

By adding equations 1 and 2 , we get

9a + 12b = -75
8a - 12b = 24
17a + 0 = - 51
17a = -51
a = -51/17
a = -3

By substituting a(-3) in equation 1 , we get

3a +4b = -25
3(-3) +4b = -25
-9 + 4b = -25
4b = -25 + 9
4b = -16
b = -16/4
b = -4

Therefore, a = -3 and
b = -4
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y = x + 2 -----> x + 2 = y ------>x - y + 2 =0-------->x - y = -2---------> equation 1

2x + y = 11 ---------> equation 2

By adding the equations 1 and 2 , we get

x - y = -2
2x + y = 11
3x + 0 = 9
3x = 9
x = 9/3
x = 3

By substituting x(3) in equation 1 ,we get

x - y = -2
3 - y = -2
- y = -2 -3
- y = -5
y = -5/-1
y = 5

Therefore, x = 3 and
y = 5
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Answer 2

3a + 4b = -25
2a - 3b = 6

9a+12b=-75 (multiplied by 3)
8a-12b=24 (multiplied by 4)
_____________
17a = -51
(I needed to cancel the 12bs so i added 12 +(-12) = 0)
a = -51/17
a = -3

sub -3 back into original equation of your choice
i'll choose second

2(-3) - 3b = 6
-6 - 3b = 6
-6 - 6 =3b (bring to other side of equals and change sign)
-12 = 3b
-12/3 = b
-4 = b

a= -3, b = -4



y = x + 2 can be written as x - y = -2

2x + y = 11
x - y= -2
__________
3x = 9
x= 3

2(3) + y = 11
6 + y = 11
y = 11 - 6
y= 5

x=3 , y =5

Answer 3

both of these problems involve a system of two equations with two unknowns. The two problems can be solved using two different methods. The first by a method known as Gaussian Elimination (sometimes simply call the elimination method) and the second by the substitution method.

In the first system you have two equations:
1) 3a + 4b = -25
2) 2a - 3b = 6

since the cooeficients of b are of opposite sign it may be easier to eliminate them in the following manner. since 12 is a common multiple of both 3 and 4 we will multiply both equations so that the cooeficient of b in each equation is 12 but with opposite signs. to do this multiply eq-1 by 3 and eq-2 by 4 which will give:
1) 9a + 12b = -75
2) 8a - 12b = 24

now if we add both equations to each other we can eliminate the b-terms

9a + 12b +8a - 12b = -75 + 24
17a = -51
so a=-3

now, you can use the fact that a=3 to solve for b by plugging in the value of a ans solving for b.

For the second system you have
y=x+2
2x+y=11

by substituting the value of y in the first equation into the second equuation you get:
2x+x+2=11
3x=9 so x=3
since y=x+2 then y=5

Answer 4

3a + 4b = -25 (multiply by 3)
2a - 3b = 6 (multiply by 4)

9a + 12b = -75
8a - 12b = 24 (now add them together)

17a + 0b = -51 (divide by 17)
a = -3

To get b, plug -3 in for a in either original equation.

2(-3) - 3b = 6 (simplify)
-6 -3b = 6 (add 6 to both sides
-3b = 12 (divide by -3)
b = -4

Check by substituting -3 for a and -4 for b in the original equations.

Now *you* do the 2'nd one. Math is like any other sport. You won't get good at it if you just set around watching other people play ☺


Doug

Answer 5

3a + 4b = -25......(1)

2a - 3b = 6.....(2
3*(1:) 9a+12b=-75/......(3)
4*(2: 8a-12b=24......(4)
(3+(4 :17a=51 or a=3. put in (1
9+4b=-25 or4b=-34, b=-8.5



2.y = x + 2or x=2y-2.put inthe other


2x + y = 11
4y-2+y=11
5y=13

y=13/5


x=26/5-2 =16/5


)

Answer 6

Mult 1st by 3 and 2nd by 4
9a + 12b = -75
8a - 12b = 24
Add
17a = -51
a = -3

b = -4

Substitute
2x + y = 11
2x + (x+2) = 11
3x + 2 = 11
3x = 9
x = 3, y = 5

Answer 7

a = -3, b = -4
x = 3, y = 5

Answer 8

try to knw the concept

Answer 9

a = -3, b = -4
x = 3, y = 5

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