Solve the system by addition
2x-4y=7
4x+2y=9
To solve the given system of equations using the method of addition (also known as elimination), follow these steps:
Step 1: Multiply one or both equations by appropriate numbers to make the coefficients of one of the variables equal or opposite in both equations. In this case, we can multiply the first equation by 2 and the second equation by 2 to make the coefficients of y equal:
1st Equation: 2(2x - 4y) = 2(7) => 4x - 8y = 14
2nd Equation: 2(4x + 2y) = 2(9) => 8x + 4y = 18
Now, the system of equations becomes:
4x - 8y = 14
8x + 4y = 18
Step 2: Add the two equations together to eliminate one variable. In this case, we can add the equations vertically:
(4x - 8y) + (8x + 4y) = 14 + 18
This simplifies to:
12x - 4y = 32
Step 3: Solve the resulting equation for the remaining variable. In this case, we solve for x:
12x - 4y = 32
12x = 32 + 4y
x = (32 + 4y) / 12
x = (8 + y) / 3
Step 4: Substitute the value of x into one of the original equations. Let's use the first equation:
2x - 4y = 7
2((8 + y) / 3) - 4y = 7
(16 + 2y) / 3 - 4y = 7
Step 5: Solve the equation obtained in Step 4 for the remaining variable. In this case, we solve for y:
(16 + 2y) / 3 - 4y = 7
16 + 2y - 12y = 21
-10y = 21 - 16
-10y = 5
y = 5 / -10
y = -1/2
Step 6: Substitute the value of y back into either of the original equations. Let's use the first equation:
2x - 4y = 7
2x - 4(-1/2) = 7
2x + 2 = 7
Step 7: Solve the equation obtained in Step 6 for x:
2x + 2 = 7
2x = 7 - 2
2x = 5
x = 5 / 2
x = 2.5
Therefore, the solution to the given system of equations is x = 2.5 and y = -0.5.