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#
Question:

Solve this system of equations:
$1617_w123_h20.png$

-6x + 10y = 14

x + 2y = 5

A
(1, 2)

Explaination

The solution is the value or set of values that satisfies each of the equations. Because lines can intersect at only one point, if there is a solution, it must be the point at which the lines intersect. Begin by finding the solution to the system of linear equations. Elimination will be used to solve for the variable *x*. Multiply the second equation by -5 and combine the two lines to solve for *x*:
(-6x + 10y = 14) + (-5x - 10y = -25), gives -11x = -11, so x = 1. Substitute this value into either linear equation to solve for *y*:
1 + 2y = 5, so y = 2
To confirm that (1, 2) is a solution, substitute it into the quadratic equation to test if it yields a true statement:
$1538_w148_h20.png$, which becomes 2 = 1 + 3 - 2, which gives 2 = 2, so the only solution is (1, 2)

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