Find the direct variation equation of a system of equations where (y = 3x + 2) and (y = 5x - 1).

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Accepted Answer

Step:1 ：Step 1: In a direct variation, the equation can be written in the form (y = kx) where (k) is the constant of variation. To find the constant of variation, we can equate the two equations.Step:2 ：Step 2: Equating the equations, we get (3x + 2 = 5x - 1)Step:3 ：Step 3: Simplifying the equation, we get (2x = 3)Step:4 ：Step 4: Solving for (x), we get (x = frac{3}{2})Step:5 ：Step 5: Substitute (x = frac{3}{2}) into the first equation (y = 3x + 2), we get (y = 3(frac{3}{2}) + 2 = frac{9}{2} + 2 = frac{13}{2})Step:6 ：Step 6: Thus, the direct variation equation is (y = frac{13}{2}x)

Answer

Step: 1 ：Step 1: In a direct variation, the equation can be written in the form (y = kx) where (k) is the constant of variation. To find the constant of variation, we can equate the two equations.Step: 2 ：Step 2: Equating the equations, we get (3x + 2 = 5x - 1)Step: 3 ：Step 3: Simplifying the equation, we get (2x = 3)Step: 4 ：Step 4: Solving for (x), we get (x = frac{3}{2})Step: 5 ：Step 5: Substitute (x = frac{3}{2}) into the first equation (y = 3x + 2), we get (y = 3(frac{3}{2}) + 2 = frac{9}{2} + 2 = frac{13}{2})Step: 6 ：Step 6: Thus, the direct variation equation is (y = frac{13}{2}x)

Find the direct variation equation of a system of equations where $y = 3 x + 2$ and $y = 5 x - 1$ .

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Popular Problems

Find the direct variation equation of a system of equations where y=3x+2 and y=5x−1.

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Popular Problems

Find the direct variation equation of a system of equations where $y = 3 x + 2$ and $y = 5 x - 1$ .