solve each system using elimination x+4y=12 and 2x-3y=6
To solve the system using elimination, we want to eliminate one variable by adding or subtracting the two equations. Let's solve the system:
1) x + 4y = 12
2) 2x - 3y = 6
Step 1: Multiply equation (1) by 2 to make the x-term in equation (1) match the x-term in equation (2):
2(x + 4y) = 2(12)
2x + 8y = 24
So now we have:
1) 2x + 8y = 24
2) 2x - 3y = 6
Step 2: Subtract equation (2) from equation (1) to eliminate the x-term:
(2x + 8y) - (2x - 3y) = 24 - 6
2x + 8y - 2x + 3y = 18
Simplifying, we get:
11y = 18
Step 3: Solve for y:
Divide both sides of the equation by 11:
11y/11 = 18/11
y = 18/11
So we have found the value of y.
Step 4: Substitute the value of y back into one of the original equations to solve for x. Let's use equation (1):
x + 4(18/11) = 12
x + 72/11 = 12
Multiply both sides of the equation by 11 to get rid of the fraction:
11x/11 + 72/11 = 12*11/11
x + 72/11 = 132/11
Now subtract 72/11 from both sides:
x + 72/11 - 72/11 = 132/11 - 72/11
x = 60/11
So we have found the value of x.
Therefore, the solution to the system of equations is x = 60/11 and y = 18/11.