If [tex]x = 2t - 9[/tex] and [tex]y = 5 - t[/tex], which of the following expresses [tex]y[/tex] in terms of [tex]x[/tex]?

A. [tex]y = -\frac{x}{2} - \frac{13}{2}[/tex]
B. [tex]y = -\frac{x}{2} + \frac{13}{2}[/tex]
C. [tex]y = -2x - 4[/tex]
D. [tex]y = 2x - 4[/tex]

To express y in terms of x, we solve the first equation for t and substitute this into the second equation. This leads us to the final** expression**: y = -x/2 + 5. ;

Answered by Qwshop | 2024-06-18

To express y in terms of x, we first write the equation for x in terms of t: x = 2t - 9. Then, solve for t by rearranging this equation to t = (x + 9) / 2. Now, substitute this expression for t into the equation for y: y = 5 - t which becomes y = 5 - ((x + 9) / 2). Simplify this expression to write y in terms of x.
After simplifying, we find that the equation y = 5 - ((x + 9) / 2) becomes y = (1/2)x - (1/2)4.5. Hence, the expression for y in terms of x is y = 0.5x - 4.5.

Answered by BishopBriggs | 2024-06-24

To express y in terms of x, we solved for t and substituted it into the equation for y, leading us to the expression y = − 2 x ​ + 2 13 ​ . Therefore, the correct answer is option B.
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Answered by Qwshop | 2024-09-03