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Identify the solution(s) of the system of equations, if any. 2x+5y=10 and y=2-x

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2 Answers

This is a classic two equations with two unknowns type problem.  The goal in the first step is to eliminate one of the variables by making an equivalent statement in terms of one variable. In order to get rid of one of the variables, substitute either

y = 2-x    or  x = 2 - y    (These equations say the same thing)

into the first equation. (It is usually easier to substitute the smaller equation into the bigger one)

Now you should have one equation with one unknown(x or y). Solve for that unknown.

Next, use that value you just got to find the other value by substituting it into either equation. If you have done everything right, both equations will give you the same answer but the smaller one will be quicker.

The solution is (x,y) as you are looking for the x and y that satisfy your two equations.

They give you an  expression for y right off the bat so substitution would be the easiest method.

if y = 2-x, then 2x +5y = 2x + 5(2-x)

2x + 10 - 5x = 10 so that -3x = 0 and x = 0

put that back into the original equation y= 2-x and you get y = 2

Solution is choice (d) : (0,2)

Another way to do multiple choice questions is to plug in the values they give you and look for validity.

Using choice (a) : (-2,0)

you'd get 2(-2) + 5(0) = 10 or -4 =10. Clearly wrong.

Choice (b): (2,0) you'd get 2(2) + 5(0) =10 or 4 = 10 Wrong again and should be kind of obvious since the only difference between a and b is a change in sign on the x value.

Choice (c): (0,-2)
 you'd get 2(0) + 5(-2) = 10 or -10 = 10, here you can see that the answer is almost there but simply needs a change in sign.

Hope that helps you out.