Question

How do you solve 3x+y=2 and 4x+y=20?

Answer 1

Hint: We will solve this question using elimination method. We can see that y-terms of both the equations are similar in magnitude and are similar in sign. So we will subtract the two equations and the y-terms will get cancelled. We will have the terms expressed in terms of x and solving further we will get the value of x. If we substitute this value of x in any of the equations given, we will get the value of y.

Complete step by step answer:
According to the question given, we have to solve for x and y, for the given set of equations using elimination method.
In this method (Elimination method), we will be solving the equations such that at first one of the variables is eliminated so that the value of the other variable can be found. And then substituting that value in any of the equations we have the values of both the variables.
We have,
\[3x+y=2----(1)\]
\[4x+y=20-----(2)\]
We can see that the y-terms in both the equations have the same magnitude and are similar in signs, so we will subtract both the equations so that y-terms get cancelled and we can find the value of x.
We have,
\[ 3x+y=2\]
\[\underline{-(4x+y=20)}\]
\[ -x=-18----(3)\]
We get the value of x as,
\[\Rightarrow x=18\]
Putting this value of x in equation (2), we get,
\[4x+y=20\]
\[\Rightarrow 4(18)+y=20\]
\[\Rightarrow 72+y=20\]
Subtracting 72 on both sides we get,
\[\Rightarrow 72+y-72=20-72
\Rightarrow y=-52\]

Therefore, x=18 and y=-52.

Note: Elimination method can also be helpful in dealing with questions having more than two equations easily. The above solution was calculated using elimination method, but we can also solve this question using substitution method or cross multiplication method. We can check if we have the correct answer or not, as follows:
The equation we have taken is 3x+y=2, now we will substitute the values of x and y we got, we have,
\[3x+y\]
\[\Rightarrow 3(18)+(-52)\]
\[\Rightarrow 54-52\]
\[\Rightarrow 2=RHS\]
Therefore, we have the correct answer, that is, x=18 and y=-52.