Answer:
(4,1)
Explanation:
Systems of equations may be solved in one of two manners: substitution and graphing. This requaests they be solved by substitution, but I'll add the graphing solution, also.
Substitution:
We want to eliminate one of the two variables to result in an expression that only has one of the two remaining. We can do that by manipluating one of the equations such that, when it is combined with the other, results in the elimination of one of the variables.
Given:
-2x-y=-9
5x-2y=18
we can multiply or divide one of the equations so that one of the terms has equal, but opposite, values. We could multiply the first equation by 2.5 so that it becomes -5x -2.5y = 9*(2.5). Then it could be added to the second to eliminate the x term.
My preference is to find a way to avoid fracticious fractions, so I will multiply the first equation by -2 so that we can eliminate y:
-2*(-2x-y =-9)
4x+2y = 18
No add this to the second equation:
4x+2y = 18
5x-2y = 18
9x = 36
x = 4
Since x = 4:
-2x-y=-9
-2*(4)-y=-9
-8 - y = -9
y = 1
The solution is (4,1). It is the point the satisfies both equations.
-2x-y=-9
-2(4)-(1)=-9
-8-1=-9 YES
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5x-2y=18
5(4)-2(1)=18
20 - 2 = 18 YES
Graphing:
The solution to these equations is the point at which the lines intersect. See the attached graph. The lines intersect at (4,1).