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For each ordered pair, determine whether it is a solution to the system of equations. [ { y=2 x-1 3 x-2 y=7 . ] multirow(2)(}{ (x, y) ) & multicolumn(2)(|c|)( Is it a solution? ) cline ( 2 - 3 ) & Yes & No (1,-2) & 0 & 0 (-5,-11) & 0 & 0 (4,7) & 0 & 0 (0,6) & 0 & 0

Question

For each ordered pair, determine whether it is a solution to the system of equations.
[
{
y=2 x-1 
3 x-2 y=7
.
]

 multirow(2)(}{ (x, y) ) & multicolumn(2)(|c|)( Is it a solution? ) 
cline ( 2 - 3 ) & Yes & No 
 (1,-2) & 0 & 0 
 (-5,-11) & 0 & 0 
 (4,7) & 0 & 0 
 (0,6) & 0 & 0

For each ordered pair, determine whether it is a solution to the system of equations. [ { y=2 x-1 3 x-2 y=7 . ] multirow(2)(}{ (x, y) ) & multicolumn(2)(|c|)( Is it a solution? ) cline ( 2 - 3 ) & Yes & No (1,-2) & 0 & 0 (-5,-11) & 0 & 0 (4,7) & 0 & 0 (0,6) & 0 & 0

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HeidiMaster · Tutor for 5 years

Answer

Let's evaluate each ordered pair to determine if it is a solution to the given system of equations.The system of equations is:1. \(y = 2x - 1\)2. \(3x - 2y = 7\)We will substitute the \(x\) and \(y\) values from each ordered pair into both equations to see if they satisfy both equations.**Ordered Pair (1, -2):**For the first equation:\(y = 2x - 1\)\(-2 = 2(1) - 1\)\(-2 = 2 - 1\)\(-2 = 1\)This is not true, so \((1, -2)\) is **not** a solution.For the second equation (even though we already know the pair is not a solution, we'll check for completeness):\(3x - 2y = 7\)\(3(1) - 2(-2) = 7\)\(3 + 4 = 7\)\(7 = 7\)This is true, but since the first equation did not hold, \((1, -2)\) is still **not** a solution.**Ordered Pair (-5, -11):**For the first equation:\(y = 2x - 1\)\(-11 = 2(-5) - 1\)\(-11 = -10 - 1\)\(-11 = -11\)This is true.For the second equation:\(3x - 2y = 7\)\(3(-5) - 2(-11) = 7\)\(-15 + 22 = 7\)\(7 = 7\)This is true.Since \((-5, -11)\) satisfies both equations, it is a **solution** to the system.**Ordered Pair (4, 7):**For the first equation:\(y = 2x - 1\)\(7 = 2(4) - 1\)\(7 = 8 - 1\)\(7 = 7\)This is true.For the second equation:\(3x - 2y = 7\)\(3(4) - 2(7) = 7\)\(12 - 14 = 7\)\(-2 = 7\)This is not true, so \((4, 7)\) is **not** a solution.**Ordered Pair (0, 6):**For the first equation:\(y = 2x - 1\)\(6 = 2(0) - 1\)\(6 = 0 - 1\)\(6 = -1\)This is not true, so \((0, 6)\) is **not** a solution.For the second equation (again, just for completeness):\(3x - 2y = 7\)\(3(0) - 2(6) = 7\)\(0 - 12 = 7\)\(-12 = 7\)This is not true, so \((0, 6)\) is still **not** a solution.**Summary of Solutions:**- \((1, -2)\): No- \((-5, -11)\): **Yes**- \((4, 7)\): No- \((0, 6)\): NoThe accurate answer is that the only solution to the system of equations from the given ordered pairs is \((-5, -11)\).
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