Answer:
(x, y) = (-3, 5)
Explanation:
There are many ways to solve a system of two equations with two unknowns. Almost all of them involve reducing the system to one equation in one unknown. (Graphical solution, as in the attachment, bypasses that algebraic manipulation.)
In general, the first step is to look at the equations to see if ...
- one is of the form x = ( ) or y = ( )
- the coefficients of one of the variables are opposites
- the coefficients of one of the variables are related by a simple number.
If the first condition is true, then the system may be easily solved by "substitution." The expression you have for one of the variables can be substituted for that variable in the other equation.
If the second condition is true, you can add the equations to eliminate the variable with opposite coefficients. (Opposites add to give zero.)
Here, the third condition holds: the coefficient of x in the first equation (4) is simply related to the coefficient of x in the second equation (8) by a factor of 2.
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So, we can eliminate the x-variable from the system of equations by multiplying the first equation by -2 and adding that result to the second equation:
-2(4x +2y) +(8x +5y) = -2(-2) +(1)
-8x -4y +8x +5y = 4 +1 . . . . eliminate parentheses
y = 5 . . . . . . . . . . . . . . . . . . . collect terms
Now, we can substitute this value into either equation to find the value of x. Using the first equation, we get ...
4x +2(5) = -2
4x = -12 . . . . . . . subtract 10
x = -3 . . . . . . . . . divide by 4
The solution to the system of equations is (x, y) = (-3, 5).