Answer
(5,-1) is not a solution.
(-1,3) is not a solution.
(2,1) is a solution.
Work Step by Step
Given a system of linear equations, we check if an ordered pair is a solution by substituting the given x and y value into the system. If both equations produce a true statement, the ordered pair is a solution and represents the intersection of both linear equations. If at least one equations produces a false statement, the ordered pair is not a solution to the system.
Consider the following system of equations.
$2x+3y=7$
$5x-y=9$
We need to first test if (5, -1) is a solution. To do so we will substitute 5 for x and -1 for y and evaluate each equation.
$2(5)+3(-1)=7$
$10-3=7$
$7=7$
True
$5(5)-(-1) = 9$
$25+1 = 9$
$26 = 9$
False
Because at least one evaluation is false, (5,-1) is not a solution.
onsider the following system of equations.
$2x+3y=7$
$5x-y=9$
We need to first test if (-1, 3) is a solution. To do so we will substitute -1 for x and 3 for y and evaluate each equation.
$2(-1)+3(3)=7$
$-2-9=7$
$7=7$
True
$5(-1)-(3) = 9$
$-5-3 = 9$
$-8 = 9$
False
Because at least one evaluation is false, (-1,3) is not a solution.
We need to first test if (2, 1) is a solution. To do so we will substitute 2 for x and 1 for y and evaluate each equation.
$2(2)+3(1)=7$
$4+3=7$
$7=7$
True
$5(2)-(1) = 9$
$10-1 = 9$
$9 = 9$
True
Because both evaluations are true, (2,1) is a solution.
