Question

Solve each of the following pairs of equations by the elimination method.1. 8x+ 5y = 9 3x+2y = 4
2. 2x + 3y = 8 4x + 6y = 7
3. 3x + 4y = 25 5x - 6y = -9

Answer 1

SOLUTION IS IN THE ATTACHMENT. Elimination method :  •In this method one variable out of the two variable is eliminated by making the coefficients of that variables equal in both the equations. •After eliminating that variable, the left equation is an equation in another variable, which can be solved easily. •Value of one variable obtained in this way can be substituted in any one of the two equations to find the value of other variable.  HOPE THIS ANSWER WILL HELP YOU…

Answer 2

Dear Student,

Solution:

1) 8x+ 5y = 9 .....eq1
3x+2y = 4 .......eq2

multiply eq 1 by 2 and 2 by 5
$2(8x + 5y) = 18 \\ 16x + 10y = 18 \: \: \: \: ...eq3 \\ \\ 15x + 10y = 20......eq4$
subtract eq3 and eq4

$16x - 15x + 10y - 10y = 18 - 20 \\ x = - 2$
put the value of x in any one equation to find value of y
$3x + 2y = 4 \\ \\ 3( - 2) + 2y = 4 \\ \\ 2y = 10 \\ y = 5$
So, x= -2 ,y = 5

2) 2x + 3y = 8 ... eq1
4x + 6y = 7....eq2

multiply eq1 by 2 and subtract both equation
$4x + 6y - (4x + 6y) = 16 - 7 \\ \\ 4x - 4x + 6y - 6y = 9 \\ 0 = 9$
it is not possible,given lines do not cut each other ( parallel lines),since they don't have any solution

3)3x + 4y = 25 ...eq1
5x - 6y = -9...eq2

multiply eq 1 by 5 and eq2 by 3 and subtract eq1-eq2

15x-15x+20y+18y= 125+27
38y = 152
y = 4
put the value of y in equation 1
3x + 4(4) = 25

3x= 25-16
3x = 9
x = 3
hope the solution helps you.