solve the system of linear equations
2x+2y=1
3x-y=6
thanks
2x+2y=1
This one is obvious. Just divide the coefficients by each other, and take any inequalities and subtract them by themselves.
3x-y=6
This one is a bit tougher. First, you need to square everything. Then add 4, subtract 7, and take the square root of it all. It may not seem right, but it IS fairly complex.
2x+2y=1
6x-2y=12
-4x=-11
x= 11/4
2(11/4)+2y=1
1-22/4=2y
-18/4=2y
-18/8=y
1st equation ---> 2x + 2y = 1
2nd equation times 2 ---> 6x - 2y = 12
add them
8x = 13
x = 13/8
sub into 1st:
2(13/8+ 2y = 1
2y = 1 - 13/4
2y = -9/4
y = -9/8
x = 13/8 , y = -9/8
To solve the system of linear equations, you can use the method of substitution or the method of elimination. I will explain how to solve it using the method of substitution.
Step 1: Solve one equation for one variable in terms of the other variable.
Let's solve the second equation for y:
3x - y = 6
y = 3x - 6
Step 2: Substitute the expression for y from Step 1 into the other equation.
Substitute y = 3x - 6 into the first equation:
2x + 2(3x - 6) = 1
2x + 6x - 12 = 1
8x - 12 = 1
Step 3: Solve the resulting equation for x.
Add 12 to both sides of the equation:
8x = 13
Divide both sides of the equation by 8:
x = 13/8
Step 4: Substitute the found value of x into one of the original equations to find y.
Using the first equation, substitute x = 13/8:
2(13/8) + 2y = 1
13/4 + 2y = 1
2y = 1 - 13/4
2y = 1/4
Divide both sides of the equation by 2:
y = 1/8
So, the solution to the system of equations is x = 13/8 and y = 1/8.