Question

8x+3y=4 -7x+5y=-34 Elimination using multiplication

Answer 1

Answer:

$x=2\\\\y=-3$

Step-by-step explanation:

Given Equations:

$8x+3y=4$             Equation :1

$-7x+5y=-34$      Equation:2

In elimination method, we makes the coefficient of any one variable same and eliminate them to get the solution in terms of the other variable.

Multiplying Equation:1 by '5' and Equation:2 by '3'

    $40x+15y=20$            Equation:3

  $-21x+15y=-102$       Equation:4

Subtracting Equation:4 From Equation:3

$(40x+15y)-(-21x+15y)=20-(-102)$

$40x+15y+21x-15y=20+102$

Adding the coefficients of same variables:

              $61x=122\\\\x=\frac{122}{61} \\\\x=2$

Putting the value of 'x' in Equation:1 to find the value of 'y'

         $8x+3y=4$

          $8(2)+3y=4\\\\16+3y=4$

Subtracting '16' both the sides:

           $3y=4-16\\\\3y=-12$

Dividing by '3' both the sides:

             $y=\frac{-12}{3}\\ \\y=-3$

So the solution of the equations is:

              $x=2\\\\y=-3$

Answer 2

Answer:

x= 2    and y = -4

Step-by-step explanation:

8x + 3y = 4 ---------------------------------(1)

-7x + 5y = -34 -----------------------------(2)

Multiply through equation (1) by 5 and multiply through equation(2) by 3

40x + 15y = 20 ----------------------------(3)

-21x + 15y =-102----------------------------(4)

Subtract equation (4) from equation (3)

61x = 122

Divide both-side of the equation by 61

61x/61 = 122/61

(At the left-hand side of the equation 61 will cancel-out 61 leaving us with just x, while at the left-hand side of the equation 122 will be divided by 61)

x = 122/61

x=2

Substitute x= 2 into equation (1)

8x + 3y = 4

8(2) + 3y = 4

16 + 3y = 4

Subtract 16 from both-side of the equation

16-16 + 3y = 4-16

3y = -12

Divide both-side of the equation by 3

3y/3 = -12/3

y = -4

x= 2    and y = -4