Question

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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.

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 $y=4x-3$.

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.