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Coefficient : In a polynomial the constants that the terms $x^n$ are multiplied with are called the coefficients of the polynomial. For example the polynomial $2x^2+3x+5$ has the coefficients 2, 3 and 5.
Equation : An equation is a mathematical statement in which two expressions are written with an equal sign in between. A solution of an equation is a set of variables that makes the statement a true statement.
Equivalent equation : Equivalent equations are equations that have the same set of solutions. Adding the same number to both sides of an equation results in an equivalent equation and so does multiplying both sides of an equation by a number that is not equal to zero.
Multiplication : Multiplication is the mathematical operation that is a shorthand for adding the same amount several times. For example $3\cdot 4=4+4+4=12.$
Solution : A solution to an equation is a choice of variables that when substituted into the equation results in a true statement.
We want to find the solution $x,y$ that solves the two following equations at the same time: $$3x+1y=12,$$ $$3x-2y=3.$$ What are the two equivalent equations we get by multiplying the first equation by 2 and the second equation by 1?