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A line has the equation x =2y+z if (3,2)...

A line has the equation `x =2y+z` if (3,2) is a point on the line what is z?

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To solve the problem step by step, we will follow the given equation and the information about the point on the line. ### Step 1: Understand the given equation The equation of the line is given as: \[ x = 2y + z \] ### Step 2: Identify the coordinates of the point We are given that the point (3, 2) lies on this line. Here, the x-coordinate is 3 and the y-coordinate is 2. ### Step 3: Substitute the coordinates into the equation Since the point (3, 2) lies on the line, we can substitute \( x = 3 \) and \( y = 2 \) into the equation: \[ 3 = 2(2) + z \] ### Step 4: Simplify the equation Now, simplify the right side: \[ 3 = 4 + z \] ### Step 5: Solve for z To find the value of \( z \), we can rearrange the equation: \[ z = 3 - 4 \] \[ z = -1 \] ### Conclusion Thus, the value of \( z \) is: \[ z = -1 \]
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