(3, -2) is a solution to the system of equations x - 2y = 7 and 2x + 3y = 0, (3, -2) is not a solution to the system of equations -x - y = -5 and 3x - 4y = 17 and (3, -2) is not a solution to the system of equations x + y = 1 and x - y = 6
<h3>How to determine the whether or not (3, -2) is a solution to the following systems?</h3>
The systems of equations are given as:
1. x - 2y = 7 and 2x + 3y = 0
2. -x - y = -5 and 3x - 4y = 17
3. x + y = 1 and x - y = 6
Next, we substitute (3, -2) for (x, y) in the system of equations.
So, we have:
<u>1. x - 2y = 7 and 2x + 3y = 0</u>
3 - 2 * -2 = 7 and 2 * 3 + 3 * -2 = 0
Evaluate
7 = 7 and 0 = 0
The above equation is true
Hence, (3, -2) is a solution to the system of equations x - 2y = 7 and 2x + 3y = 0
<u>2.- x - y = -5 and 3x - 4y = 17</u>
-3 + 2 = -5 and 3 * 3 + 4 * 2 = 17
Evaluate
- 1 = - 5 and 1 7 = 1 7
The above equation is false
Hence, (3, -2) is not a solution to the system of equations -x - y = -5 and 3x - 4y = 17
<u>3. x + y = 1 and x - y = 6</u>
3 - 2 = 1 and 3 + 2 = 6
Evaluate
1 = 1 and 5 = 6
The above equation is false
Hence, (3, -2) is not a solution to the system of equations x + y = 1 and x - y = 6
Read more about system of equations at:
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. Now we can factor to find the solutions. What we ask ourselves here is "What 2 numbers will add to be +4 and multiply to be -21?" +7 and -3 work because 7-3 = 4 and 7 * -3 = -21. So our factors are (x+7)(x-3). Our solutions, however, are found using the Zero Product Property. If x + 7 = 0, then x = -7. If x - 3 = 0, then x = 3. So our solutions are x = -7 and x = 3.