Solve the system by addition.
2x – 4y = 7,4x + 2y = –1
can you show me how to set it up so I can use this one as a guide.thank you
Sure.
2x - 4y = 7
4x + 2y = -1
Double both sides of the last equation.
8x + 4y = -2
Add the first and third equations (both sides separately). This results in
10x = 5
Divide both sides by 2
x = 1/2. Finally substitute x=1/2 into any of the equations
1 - 4y = 7
4y = -6
y = -3/2
To solve the system of equations using the method of addition, you need to eliminate one variable by adding or subtracting the equations. Here's how you can set it up step by step:
Step 1: Rearrange the equations
Rearrange both equations so that the variables line up.
The original equations are:
2x - 4y = 7 ...(Equation 1)
4x + 2y = -1 ...(Equation 2)
Step 2: Multiply to obtain the same coefficient
In order to eliminate one variable, you need to make the coefficient of either x or y the same in both equations. In this case, it would be convenient to eliminate y. To do this, we multiply Equation 1 by 2 and Equation 2 by 4.
Multiply Equation 1 by 2:
2 * (2x - 4y) = 2 * 7
4x - 8y = 14 ...(Equation 3)
Multiply Equation 2 by 4:
4 * (4x + 2y) = 4 * (-1)
16x + 8y = -4 ...(Equation 4)
Step 3: Add the equations
Add Equation 3 and Equation 4 together. This will eliminate the y variable.
(4x - 8y) + (16x + 8y) = 14 + (-4)
4x + 16x - 8y + 8y = 10
20x = 10
Simplifying the equation gives you:
20x = 10
Step 4: Solve for x
Divide both sides of the equation by 20 to solve for x:
x = 10/20
x = 1/2
Step 5: Substitute the value of x into one of the original equations
Now that you have the value of x, substitute it into either Equation 1 or Equation 2 to find the corresponding y value. Let's use Equation 1.
2(1/2) - 4y = 7
1 - 4y = 7
Subtract 1 from both sides:
-4y = 6
Divide both sides by -4 to solve for y:
y = 6 / -4
y = -3/2
Step 6: Check your solution
To confirm that the solution is correct, substitute the values of x and y back into both original equations. If the left-hand side of each equation equals the right-hand side, then the solution is correct.
Checking Equation 1:
2(1/2) - 4(-3/2) = 7
1 + 6 = 7 [Both sides are equal]
Checking Equation 2:
4(1/2) + 2(-3/2) = -1
2 - 3 = -1 [Both sides are equal]
Both equations check out, so the solution to the system of equations is:
x = 1/2
y = -3/2