Question

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

Answer 1

Answer:

x = 0 and y = 3 respectively

Step-by-step 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

Answer 2

We have the following system of equations,

$\begin{cases}8x+2y=6 \\2x+3y=9 \\\end{cases}$

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,

$\begin{cases}24x+6y=18 \\-4x-6y=-18\end{cases}$

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.