When using substitution to solve this system of equations, what is the result of the first step? x = 6y + 3,x + 2y = 5

Question

A.x + 2y + 6y = 3 + 5

B.x + 2 (6y + 3) = 5

C.(6y + 3) + 2y = 5

D.none of these

Answer 1

x = 6y + 3

x+2y = 5, replace x by 6y+3

(6y+3) + 2y = 5

8y = 5-3 = 2

y = 2/8= 1/4= 0.25

x = 6y+3 = 6(1/4) +3 = 3/2 + 3 = 9/2 = 4.5

C is correct

A and B are clearly wrong and would lead to incorrect answers

You could have substituted a value for y in terms of x, but neither equation is solved for y, so that would require another step. x+2y = 5, solve for y: y =(5-x)/2 then replace y in x = 6y + 3 to get x =6(5-x)/2 + 3

x= 15 - 3x + 3

4x = 18

x= 18/4 = 9/2 = 4.5

y=(5-4.5)/2 = .5/2 = .25

D is wrong, even though there is another way to solve the problem, by substitution. For D to be right, neither A,B or C can be right, but C is correct.

the point of substitution method is to eliminate one variable, so you're left with just one variable. A and B fail to do that.. The solution is x=9/2 and y= 1/4. Plug those values into the 1st two original equations and they work. Plug them into the C equation and they work. plug them into the A or B equations and they don't work.