Solve the set of equations 3x - 8y = 10 and 2x + 3y = 6
4 Answers
sciencesolve | Teacher | (Level 3) Educator Emeritus
You may use matrices to solve the system, hence, you need to create the matrix of coefficients of variables, such that:
A = ((3,-8),(2,3))
You need to evaluate the determinant of the matrix A, such that:
`det A = [(3,-8),(2,3)]` => `det A = 9 + 16 => detA = 25`
You need to use Cramer's formulas to evaluate x and y, such that:
`x = (Delta_x)/(det A); y = (Delta_y)/(det A);`
`Delta_x = [(10,-8),(6,3)]` => `Delta_x =30 + 48 = 78`
`x = 78/25`
`Delta_y = [(3,10),(2,6)]` =>` Delta_y = 18 - 20 = -2`
`y = -2/25`
Hence, evaluating the solution to the system of equations, using Cramer's formulas, yields `x = 78/25, y = -2/25` .
justaguide | College Teacher | (Level 2) Distinguished Educator
The system of equations consisting of 3x - 8y = 10 and 2x + 3y = 6 has to be solved for x and y.
3x - 8y = 10
=> 3x = 10 + 8y
=> x = 10/3 + (8y)/3
Substitute this for x in 2x + 3y = 6
=> 2*(10/3 + (8y)/3) + 3y = 6
=> 20/3 + (16*y)/3 + 3y = 6
=> (25y)/3 = 6 - 20/3
=> 25y = -2
=> y = -2/25
x = 10/3 + (8y)/3 = 10/3 - 16/75 = 78/25
The solution of the given set of equations is x = 78/25 and y = -2/25
malkaam | Student, Undergraduate | (Level 1) Valedictorian
Hide Replies ▲
malkaam | Student, Undergraduate | (Level 1) Valedictorian
Sorry posted this one by accident.
malkaam | Student, Undergraduate | (Level 1) Valedictorian
3x - 8y = 10 ------eq(i)
2x + 3y = 6 ------eq(ii)
To find the value of x and y we can use the substitution method by considering eq (i) to isolate y:
3x - 8y = 10
-8y=10-3x
y=(10-3x)/-8
y=-(-10+3x)/-8
On cancelling off the minus signs we get:
y= (-10+3x)/8
y= -10/8 + 3x/8
Putting this value in eq(ii):
2x + 3{-10/8 + 3x/8} = 6
Multiplying 3 with each component in the bracket:
2x -30/8 + 9x/8 = 6
Taking 8 as L.C.M.:
{16x -30 +9x}/8 = 6
Taking 8 on right hand side:
16x - 30 +9x = 6*8
16x - 30 +9x = 48
25x - 30 = 48
25x = 48 +30
25x = 78
x=78/25
Putting value of x in eq(i) to find out y:
3x - 8y = 10
3(78/25) - 8y = 10
234/25 - 8y = 10
taking 234/25 on the right hand side:
-8y = 10 - 234/25
Taking 25 as L.C.M:
-8y = {250-234}/25
-8y = 16/25
Taking -8 on right hand side:
y = -16/25*-8
y = -16/200
y = -2/25
Therefore: x=78/25 and y = -2/25