# Solve the follwoing : 2a - 5b = 3 and 3a+b = 4

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2a - 5b = 3 ...........(1)

3a + b = 4.................(2)

We will solve the system usin the substitution method.

From (2) we will rewrite:

3a + b = 4

==> b= 4 - 3a

Now we will subiute b value in (1):

2a-5b = 3

==> 2a - 5(4-3a) = 3

=> 2a - 20 + 15a = 3

=> 17a = 23

**==> a= 23/17 **

Now to find b, we will substitute:

==> b= 4 - 3a

= 4 - 3(23/17)

= 4- 69/17

= (68-69)/17

= -1/17

**==> b= -1/17**

2a - 5b = 3 (1)

3a+b = 4 (2)

We'll multiply (2) by 5 and we'll add it to (1)

2a - 5b + 15a + 5b = 3 + 20

We'll combine and eliminate like terms:

17a = 23

We'll divide by 17:

**a = 23/17**

We'll substitute a in (1):

2a - 5b = 3

2*23/17 - 5b = 3

46/17 - 5b = 3

46/17 - 3 = 5b

(46 - 17*3)/17 = 5b

(46-51)/17 = 5b

-5/17 = 5b

We'll divide by 5 both sides:

**b = -1/17**

The solution of the system is:{23/17 ; -1/17}

2a - 5b = 3

3a + b = 4

Multiply everything in the second equation by 5

By multiplying, your equation should look like

** 2a - 5b = 3**

**15a + 5b = 20 **now, add -5b with 5b (which means add 2a with 15a and 3 with 20 )

By adding, your equation should look like

**17a = 23 **divide both sides by 17

By dividing, your equation should look like

**a = 23/17 **which is your answer for " a "

Now plug 23 /17 into one of the equation

**3 (23/17) + b = 4 **now multiply 23/17 with 3

By multiplying, your equation should look like

**69/17 + b = 4 **now, subtract 69/17 on both sides

By subtracting, you should get

** = -1/17 **which is your answer for " b "

So your answer is **a = 23/17 ; b = -1/17**

2a-5b=3

2a-5b=3+5b

2a=3+5b

2a/2=3/2+5/2b

a=3/2+5/2b

3(3/2+5/2b)+b=4

9/2+15/2b+b=4

9/2+15/2b+b-9/2=4-9/2

15/2b+b=-1/2

17/2b=-1/2

(17/2b)/17/2=(-1/2)/17/2

b=-1/17

2a-5(-1/17)=3

2a+5/17=3

2a+5/17-5/17=3-5/17

2a=46/17

2a/2=(46/17)/2

a=23/17

in order to do this you must simultaneously solve it

1) Find the value of b

b=4-3a

2) Subsitute b into 2a-5b=3 and solve to find value of a

2a-5(4-3a)=3

2a-20+15a=3

17a=23

a=23/17

4)Sub. a into either one of the formulas and solve to find the value of b

2a-5b=3

2x(23/17)-5b=3

46/17-5b=3

-5b=5/17

b=-1/17

therefore a= 23/17 and b=-1/17

To solve :

2a -5b = 3...(1)

3a+ b= 4.....(2)

Eq(1) +5eq(2) gives: 2a+5*3a = 3+5*4 = 23

17a = 23. So a = 23/17.

Put a = 23/17 in (1): 2* 23/17 - 5b = 3.

Therefore 5 b = 2*23/17-3 = 46/17 -51/17 = -5/17

b = (-5/17)/5 = -1/17.

Therefore a = 23/17 and b = -1/17.