Answer: To find an equivalent system of equations, we can use algebraic operations to manipulate the original equations while preserving the solutions.
One way to eliminate one of the variables is to multiply one of the equations by a constant that will make the coefficients of one of the variables in the two equations opposite in sign. Here, we can multiply the first equation by -5 and the second equation by 2 to eliminate the x variable:
-10x - 20y = -20
10x - 10y = 10
Adding these two equations, we get:
-30y = -10
Dividing both sides by -30, we get:
y = 1/3
Substituting this value of y into one of the original equations, we can solve for x:
2x + 4(1/3) = 4
2x + 4/3 = 4
2x = 8/3
x = 4/3
Therefore, an equivalent system of equations is:
x = 4/3
y = 1/3
These two equations have the same solution as the original system.
Explanation: