How many solutions does the system of equations below have? y = x + 1/3 y = 9/2x − 9/5 Choices: (A)no solution (B)one solution (C)infinitely many solutions

Set Equations Equal: Step 1: Set the equations equal to each other to find the intersection point. y = x + 1/3 y = 9/2x - 9/5 Set x + 1/3 = 9/2x - 9/5 Solve for x: Step 2: Solve for x. x + 1/3 = 9/2x - 9/5 To eliminate fractions, multiply every term by 10 (the least common multiple of 2, 3, and 5): 10x + 10/3 = 45x - 18/5 Now, simplify and solve for x: 10x + 3.33 = 45x - 3.6 35x = 6.93 x = 6.93 / 35 x ≈ 0.198

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How many solutions does the system of equations below have? $\newline$ $y = x + \frac{1}{3}$ $\newline$ $y = \frac{9}{2}x - \frac{9}{5}$ $\newline$ Choices: $\newline$ (A)no solution $\newline$ (B)one solution $\newline$ (C)infinitely many solutions

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Math Problems

Grade 8

Find the number of solutions to a system of equations

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Q. How many solutions does the system of equations below have?

\newline

y = x + \frac{1}{3}

\newline

y = \frac{9}{2}x - \frac{9}{5}

\newline

Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

Set Equations Equal: Step $1$ : Set the equations equal to each other to find the intersection point. $\newline$ $y = x + \frac{1}{3}$ $\newline$ $y = \frac{9}{2}x - \frac{9}{5}$ $\newline$ Set $x + \frac{1}{3} = \frac{9}{2}x - \frac{9}{5}$
Solve for x: Step $2$ : Solve for x. $\newline$ $x + \frac{1}{3} = \frac{9}{2}x - \frac{9}{5}$ $\newline$ To eliminate fractions, multiply every term by $10$ (the least common multiple of $2$ , $3$ , and $5$ ): $\newline$ $10x + \frac{10}{3} = 45x - \frac{18}{5}$ $\newline$ Now, simplify and solve for x: $\newline$ $10x + 3.33 = 45x - 3.6$ $\newline$ $35x = 6.93$ $\newline$ $x = \frac{6.93}{35}$ $\newline$ $x \approx 0.198$