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Question
Using the substitution method determine if (-2, -4) is a solution to the following system of linear equations.
−4x+3y=−4
−3x+2y=−2
(1 point)
Responses
True, because substituting the given ordered pair yields two true equations.
True, because substituting the given ordered pair yields two true equations.
False, because substituting the given ordered pair does not yield two true expressions.
To determine if (-2, -4) is a solution, we need to substitute the values of x and y into both equations and see if the resulting expressions are true. Let's do that:
Substituting x = -2 and y = -4 into the first equation:
-4(-2) + 3(-4) = -4
8 - 12 = -4
-4 = -4 (true)
Substituting x = -2 and y = -4 into the second equation:
-3(-2) + 2(-4) = -2
6 - 8 = -2
-2 = -2 (true)
Since substituting the values of x = -2 and y = -4 into both equations yield true expressions, the statement "True, because substituting the given ordered pair yields two true equations" is correct.