# Systems.Solve the following system:  2a - 5b = 3        3a+b = 4

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to solve the system of equations:

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

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

(1) + 5*(2)

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

=> 17a = 23

=> a = 23/17

Substitute in (2)

=> b = 4 - 3*(23/17)

=> b = (68 - 69)/17

=> b = -1/17

The solution of the equations is a = 23/17 and b = -1/17

tonys538 | Student, Undergraduate | (Level 1) Valedictorian

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The system of equations

2a - 5b = 3

3a+b = 4

has to be solved.

From 3a + b = 4, express b in terms of a. This gives b = 4 - 3a

Substitute for b in 2a - 5b = 3

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

2a - 20 + 15a = 3

17a = 23

a = 23/17

b = 4 - 3a = 4 - 3*(23/17) = 4 - 69/17 = -1/17

The solution of the given system of equation is a = 23/17 and b = -1/17

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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}