Q. Which ordered pair is a solution of the equation?3x+3y=−x+5yChoose 1 answer:(A) Only (1,2)(B) Only (2,4)(C) Both (1,2) and (2,4)(D) Neither
Combine like terms: Simplify the equation by combining like terms.We need to get all the x terms on one side and all the y terms on the other side.3x+3y=−x+5yAdd x to both sides:3x+x+3y=5y4x+3y=5yNow, subtract 3y from both sides:4x=5y−3y4x=2y
Isolate x and y terms: Solve for y in terms of x.To find the relationship between x and y, we divide both sides by 2:24x=22y2x=y
Solve for y in terms of x: Check the ordered pairs to see if they satisfy the equation 2x=y.For (A) (1,2):Substitute x=1 and y=2 into the equation:2(1)=22=2This is true, so (1,2) is a solution.
Check solution (1,2): Check the ordered pair (B) (2,4).Substitute x=2 and y=4 into the equation:2(2)=44=4This is also true, so (2,4) is a solution.
Check solution 2,4: Determine the final answer based on the solutions found in steps 3 and 4.Since both ordered pairs 1,2 and 2,4 satisfy the equation 2x=y, the correct answer is (C) Both 1,2 and 2,4.
More problems from Does (x, y) satisfy the linear equation?