Keywords:
Systems of equations, variables, values, steps
For this case we have a system of two equations with two variables given by "x" and "y" respectively. We must solve the system by finding the values of the variables. For this, we follow the steps below:
[tex]6x - 3y = 3\ (1)\\-2x + 6y = 14\ (2)[/tex]
Step 1:
We multiply the second equation by 3:
[tex]3 * (- 2x + 6y = 14)\\-6x + 18y = 42[/tex]
Step 2:
We add both equations:
[tex]6x - 3y = 3\\-6x + 18y = 42\\-6x + 6x-3y + 18y = 42 + 3\\15y = 45[/tex]
[tex]y = \frac {45} {15}\\y = 3[/tex]
Step 3:
We substitute[tex]y=3[/tex] in the first equation:
[tex]6x - 3 (3) = 3\\6x-9 = 3\\6x = 3 + 9\\6x = 12\\x = \frac {12} {6}x = 2[/tex]
Thus, the solution of the system is given by [tex](x, y) = (2,3)[/tex]
Answer:
The second equation must be multiplied by "3" to eliminate the terms of the "x" when added with the first equation
The first equation must be multiplied by "2" to eliminate the terms of the "y" when added with the second equation
The system solution is given by [tex](x, y) = (2,3)[/tex]
