Solution:
Challenge: Find the solution to the system of equations:
6x + 3y = 12
9x + 12y = 28
Strategy: Eliminate one variable (y) and solve for the remaining variable (x).
step:
Align the coefficients of y: Make the coefficients of y the same in both equations.
Multiply the first equation by 4: 24x + 12y = 48
Keep the second equation as it is: 9x + 12y = 28
Eliminate y: Subtract the second equation from the first equation to eliminate y:
(24x + 12y) – (9x + 12y) = 48 – 28
Simplify: 15x = 20
Solve for x: Divide both sides by 15:
x = 20/15
x = 4/3
Substitute x into the original equation: Choose one of the original equations, let's use the first one:
6x + 3y = 12
Replace x with 4/3: 6(4/3) + 3y = 12
Solve for y:
8 + 3y = 12
3y = 4
y = 4/3
Solution: The solution of the system of equations is x = 4/3 and y = 4/3.
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