Answer:
(x, y) = (1, 5)
Explanation:
You want to solve the simultaneous equations ...
Solution
There are many ways to solve a pair of linear equations. They are often nicely solved by graphing using a graphing calculator. The graph in the attachment shows the solution is (x, y) = (1, 5).
Substitution
The first equation gives an expression for y, so it is convenient to use that in the second equation:
x -(2x +3) = -4 . . . . . . . . substitute 2x+3 for y
-x -3 = -4 . . . . . . . . . . simplify
-x = -1 . . . . . . . . . . add 3 to both sides
x = 1 . . . . . . . . . multiply both sides by -1
Now, we can use the expression for y to find y:
y = 2(1) +3 = 5
The solution is x = 1, y = 5.
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Additional comment
Of the many choices for methods of solution, often a suitable method will reveal itself when you look at the equations. Substitution works well if one of the equations gives an expression for one variable in terms of the other (as here), or if it can be solved easily for one of the variables. (For example, the second equation can be solved for x by adding y to both sides: x = y -4.)
The method called "elimination" or "addition" works well if the equations are of the same form, and one of the variables in one equation has a coefficient that is opposite of the coefficient of that variable in the other equation. Rearranging the first equation to y -2x = 3 makes the equation pair be ...
and we notice y has coefficients of +1 and -1 in the two equations, which are opposites. When we add these two equations together, we get ...
(y -2x) +(x -y) = (3) +(-4)
-x = -1 . . . . . . . simplified. The y-variable has been "eliminated."
The way to do this is to become familiar with at least a couple of different methods of solving the equations, so you can use your initial examination to choose one that works well with the equations you have.