Question

Solve the Equations
8x+2y=6
2x+3y=9

Answer 1

We have the following system of equations,

`</p><p>\begin{cases}</p><p>8x+2y=6 \\</p><p>2x+3y=9 \\</p><p>\end{cases}</p><p>`

We have to find the intersection of these two lines namely point
`P(x,y)`.

Use elimination method to solve this system of equations.

Multiply the first equation by 3 and second equation by -2 to get,

`</p><p>\begin{cases}</p><p>24x+6y=18 \\</p><p>-4x-6y=-18</p><p>\end{cases}</p><p>`

Add the equations and obtain,

`20x=0\implies x=0`.

Now plug in the 0 we just obtained to one of the original equations, note that I will insert the value in first one to get,

`2y=6\implies y=3`.

So the solution is point
`P(0,3)`.

Hope this helps.

Answer 2

x = 0 and y = 3 respectively

Explanation:

in order to solve this system of equation we would say that let

8x+2y=6...........................................................................equation 1

2x+3y=9 ...........................................................................equation 2

from equation 1

8x+2y=6...........................................................................equation 1

2y = 6 - 8x

divide both sides by 2

2y/2 = 6-8x/2

y = ( 6- 8x)/2.................................................................. equation 3

substitute for equation 3 in equation 2

2x+3y=9 ...........................................................................equation 2

2x + 3 [( 6 - 8x)/2] = 9

2x + (18 - 24x )/2 = 9

multiply through by 2

4x + 18 -24x = 18

collect the like terms

24x - 4x = 18 -18

20x = 0

divide both sides by 20

20x/20 = 0/20

x = 0

put the value of x = 0 into equation 3

y = ( 6- 8x)/2.................................................................. equation 3

y = 6 - 8(0) / 2

y = 6 - 0/2

y = 6/2

y = 3

therefore the value of x = 0 and y = 3 respectively