Sovi AI

Aufgabe

Lösungsschritte

1. Understand the question

   is (x, y) a correct solution for the system of equations?
   directions: substitute the x and y - coordinates into each equation. determine if the coordinates work for both equations (meaning it is a correct solution). if the coordinates do not work, then it is not a correct solution to the system. circle the correct selection for each problem.

   1. (1,3)

   $2x + y = 5$
   $-2x + y = 1$
   yes, (1, 3) is a correct solution to the system.
   no, (1, 3) is not a correct solution to the system.

   1. (4,0)

   $x - 2y = 4$
   $3x + y = 6$
   yes, (4, 0) is a correct solution to the system.
   no, (4, 0) is not a correct solution to the system.

   1. (2,4)

   $-3x + 2y = 2$
   $y = -3x - 2$
   yes, (2, 4) is a correct solution to the system.
   no, (2, 4) is not a correct solution to the system.

   1. (-3,8)

   $x - 2y = -19$
   $5x + 2y = 1$
   yes, (-3, 8) is a correct solution to the system.
   no, (-3, 8) is not a correct solution to the system.

   1. (4,5)

   $y = \\frac{1}{2}x + 5$
   $y = 4x - 3$
   yes, (4, 5) is a correct solution to the system.
   no, (4, 5) is not a correct solution to the system.

2. Explanation

   Step1: Test (1,3) in first system

   First equation: $2(1) + 3 = 2 + 3 = 5$, which matches $2x+y=5$.
   Second equation: $-2(1) + 3 = -2 + 3 = 1$, which matches $-2x+y=1$.

   Step2: Test (4,0) in second system

   First equation: $4 - 2(0) = 4$, which matches $x-2y=4$.
   Second equation: $3(4) + 0 = 12
   eq 6$, does not match $3x+y=6$.

   Step3: Test (2,4) in third system

   First equation: $-3(2) + 2(4) = -6 + 8 = 2$, which matches $-3x+2y=2$.
   Second equation: $-3(2) - 2 = -6 - 2 = -8
   eq 4$, does not match $y=-3x-2$.

   Step4: Test (-3,8) in fourth system

   First equation: $-3 - 2(8) = -3 - 16 = -19$, which matches $x-2y=-19$.
   Second equation: $5(-3) + 2(8) = -15 + 16 = 1$, which matches $5x+2y=1$.

   Step5: Test (4,5) in fifth system

   First equation: $\frac{1}{2}(4) + 5 = 2 + 5 = 7
   eq 5$, does not match $y=\frac{1}{2}x+5$.
   Second equation: $4(4) - 3 = 16 - 3 = 13
   eq 5$, does not match $y=4x-3$.

3. Final answer
   1. Yes, (1, 3) is a correct solution to the system.
   2. No, (4, 0) is not a correct solution to the system.
   3. No, (2, 4) is not a correct solution to the system.
   4. Yes, (-3, 8) is a correct solution to the system.
   5. No, (4, 5) is not a correct solution to the system.

Antwort

Question Analysis

OCR Text

is (x, y) a correct solution for the system of equations?
directions: substitute the x and y - coordinates into each equation. determine if the coordinates work for both equations (meaning it is a correct solution). if the coordinates do not work, then it is not a correct solution to the system. circle the correct selection for each problem.
1. (1,3)
$2x + y = 5$
$-2x + y = 1$
yes, (1, 3) is a correct solution to the system.
no, (1, 3) is not a correct solution to the system.
2. (4,0)
$x - 2y = 4$
$3x + y = 6$
yes, (4, 0) is a correct solution to the system.
no, (4, 0) is not a correct solution to the system.
3. (2,4)
$-3x + 2y = 2$
$y = -3x - 2$
yes, (2, 4) is a correct solution to the system.
no, (2, 4) is not a correct solution to the system.
4. (-3,8)
$x - 2y = -19$
$5x + 2y = 1$
yes, (-3, 8) is a correct solution to the system.
no, (-3, 8) is not a correct solution to the system.
5. (4,5)
$y = \\frac{1}{2}x + 5$
$y = 4x - 3$
yes, (4, 5) is a correct solution to the system.
no, (4, 5) is not a correct solution to the system.

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