Question 41272: please simplify and solve
1. 4x+y=2
x+2y=4
2. -x-5y=-6
3x+y=4
3. -3x+2y=7
x+y=-7
4.2x+3y=5
-x+2y=1
5.-x+2y=-6
4x-3y=4
6.4x+y=-6
3x-2y=1
Answer by zeynep(43)   (Show Source):
You can put this solution on YOUR website! 1. 4x+y=2
x+2y=4
Let's multiply the first equation by -2 to create opposite coefficients for y.
-8x-2y=-4
x+2y= 4
Now when we add these equations side by side, we will drop out y.
-7x + 0 = 0
-7x = 0 (divide each side by -7)
-7x/-7 = 0/-7
x = 0
To find the value of y, we will insert the value of x in the first equation(you may insert it into the second equation as well);
4.0+y = 2
0+y = 2
y=2
2. -x-5y=-6
3x+y=4
Let's multiply the first equation by 3 to create opposite coefficients for x;
-3x-15y=-18
3x+y=4
Now when we add the two equations side by side we will drop out x;
0-14y = -14
-14y = -14 (divide each side by -14)
14y/-14 = -14/-14
y = 1
Now let's insert the value of y into the second equation to find the value of x;
3x+1=4 (move 1 to the right of the equation)
3x= 4-1
3x=3 (divide each side by 3)
3x/3=3/3
x=1
As you see, to solve these kinds of equations we try to leave out one of the variables. To do this;
1. multiply one or both of the equations by a number that will create opposite coefficients for either x or y.
2. add the equations side by side.
3. Now you are left with one variable. Solve the equation for remaining variable.
4. Plug the value you found in the third step in on eof the given equations and find the other variable.
I hope this helps and you can solve the remaining questions. If you cannot, let me know.
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