solve each system by substitution
1.
6x-3y=-33
2xty=-1
2.
2x-y=7
3x-2y=10
3.
4x=8y
2x+5y=27
http://www.purplemath.com/modules/systlin4.htm
To solve each system of equations by substitution, follow these steps:
1. Express one variable in terms of the other in one of the equations.
2. Substitute the expression from step 1 into the other equation.
3. Solve the resulting equation for the remaining variable.
4. Substitute the value of the remaining variable back into one of the original equations to find the value of the first variable.
5. Write the solution as an ordered pair (x, y).
Let's apply these steps to each system:
1.
Equation 1: 6x - 3y = -33
Equation 2: 2xty = -1
Step 1: Express one variable in terms of the other.
From Equation 2, we have 2xty = -1. Solving for (ty), we get ty = -1/(2x).
Step 2: Substitute the expression from Step 1 into Equation 1.
Replace ty in Equation 1 with -1/(2x):
6x - 3(-1/(2x)) = -33
Step 3: Solve the resulting equation for the remaining variable.
Multiply through by 2x to clear the fraction:
12x² - 3 = -66x
Rearrange the equation:
12x² + 66x - 3 = 0
Step 4: Solve the quadratic equation.
Using factoring, quadratic formula, or completing the square, find the solutions for x. Let's assume the solutions are x1 and x2.
Step 5: Substitute the values of x1 and x2 back into one of the original equations to find the corresponding values of y.
Repeat these steps for the other systems of equations.