Question

Which is an equivalent equation to 2x + 4y = 12?

a. 10x + 20y = 60
b. 4x + 8y = 12
c. 4x + 4y = 24
d. 6x + 12y = 48

Answer 1

The equivalent equation to 2x + 4y = 12 is option (a) 10x + 20y = 60, because when divided by 5, it reduces to the original equation.

Step-by-step explanation:

The given equation is 2x + 4y = 12. To find an equivalent equation, we can multiply both sides of the equation by the same non-zero number. All terms in the original equation should be multiplied by this number to maintain equality. Let's examine the provided options:

• (a) 10x + 20y = 60: If we divide each term by 5, we get 2x + 4y = 12, which is the same as the original equation.
• (b) 4x + 8y = 12: This equation is not equivalent because dividing by 2 gives us 2x + 4y = 6, which is not the same as the original equation.
• (c) 4x + 4y = 24: This equation is not equivalent because dividing by 2 gives us 2x + 2y = 12, which is not the same as the original equation.
• (d) 6x + 12y = 48: This equation is not equivalent because dividing by 3 gives us 2x + 4y = 16, which is not the same as the original equation.

Therefore, the equivalent equation to 2x + 4y = 12 is option (a) 10x + 20y = 60.