how do you solve by elimination?
6x+4y=6
6x+2y=12
Need to know how please so I can do other problems that are similar
To solve a system of equations by elimination, follow these steps:
Step 1: Set up the equations in standard form.
Given equations:
6x + 4y = 6 ---(1)
6x + 2y = 12 ---(2)
Step 2: Multiply one or both equations by appropriate numbers to create the same coefficient for one of the variables.
In this case, we can multiply equation (2) by 2 to make the coefficient of y the same as that in equation (1). This will make it easier to eliminate one of the variables.
Multiply equation (2) by 2:
2(6x + 2y) = 2(12)
12x + 4y = 24 ---(3)
Step 3: Now, add or subtract the two equations to eliminate one variable.
Subtract equation (3) from equation (1):
(6x + 4y) - (12x + 4y) = 6 - 24
-6x + 0y = -18
-6x = -18
Step 4: Solve for the remaining variable.
Divide both sides of the equation by -6:
-6x / -6 = -18 / -6
x = 3
Step 5: Substitute the value of x into one of the original equations and solve for the other variable.
Let's use equation (1):
6(3) + 4y = 6
18 + 4y = 6
Step 6: Solve for y.
Subtract 18 from both sides of the equation:
18 + 4y - 18 = 6 - 18
4y = -12
Divide both sides of the equation by 4:
4y / 4 = -12 / 4
y = -3
Step 7: Check the values obtained by substituting them into the other equation.
Let's use equation (2):
6(3) + 2(-3) = 12
18 - 6 = 12
12 = 12
Both sides of the equation are equal, so the solution is correct.
Therefore, the solution to the system of equations is x = 3 and y = -3.
To solve similar problems, follow these steps: set up the equations, manipulate them if necessary to get the same coefficient for one variable, eliminate one variable, solve for the remaining variable, substitute the value into one of the equations and solve for the other variable, and finally, check the solution by substituting it back into the original equations.