Question
Solve the system of equations by any method. \[ -2 x+5 y=-21 \] Enter the exact answer as an ordered pair, \( (x, y) \). If there is no solution, enter NS. If there is an infinite number of solutions, enter the genera an ordered pair in terms of \( x \). Include a multiplication sign between symbols. For example, \( a * x \).
Ask by Lindsey Chang. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution is \( (x, \frac{2}{5}x - \frac{21}{5}) \).
Solution
We are given the single linear equation
-2 * x + 5 * y = -21.
Since this is one equation in two unknowns, there are infinitely many solutions. We can solve for y in terms of x.
Step 1. Isolate y:
-2 * x + 5 * y = -21
5 * y = 2 * x - 21
y = (2 * x - 21) / 5
= (2/5) * x - 21/5.
Step 2. Write the solution as an ordered pair:
(x, (2/5) * x - 21/5)
where x can be any real number.
Thus, the general solution is:
(x, (2/5) * x - 21/5).
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Simplify this solution Beyond the Answer
To solve the system of equations given by \[ -2x + 5y = -21, \] let's manipulate this equation to express it in terms of \(y\). First, we can isolate \(y\) by adding \(2x\) to both sides: \[ 5y = 2x - 21. \] Now, divide each term by 5 to solve for \(y\): \[ y = \frac{2}{5}x - \frac{21}{5}. \] This represents a linear relationship between \(x\) and \(y\). Since this is only one equation and we need another to find a unique solution, if we assume no further constraints for \(x\), we can express the infinite solution scenario as follows: Thus, the general ordered pair solution in terms of \(x\) is: \[ (x, \frac{2}{5} * x - \frac{21}{5}). \]
