To solve the equation \(3x - y = 10\), we can try to express one variable in terms of the other or find specific values that satisfy the equation. Here are a few methods:
### Solving for \(y\) in terms of \(x\):
1. Start with the given equation:
\[
3x - y = 10
\]
2. Isolate \(y\):
\[
-y = 10 - 3x
\]
3. Multiply both sides by -1 to solve for \(y\):
\[
y = 3x - 10
\]
So, \(y\) can be expressed as \(y = 3x - 10\).
### Finding specific solutions:
To find specific pairs \((x, y)\) that satisfy the equation, you can choose values for \(x\) and then compute the corresponding \(y\).
1. If \(x = 0\):
\[
y = 3(0) - 10 = -10 \quad \Rightarrow \quad (0, -10)
\]
2. If \(x = 2\):
\[
y = 3(2) - 10 = 6 - 10 = -4 \quad \Rightarrow \quad (2, -4)
\]
3. If \(x = 4\):
\[
y = 3(4) - 10 = 12 - 10 = 2 \quad \Rightarrow \quad (4, 2)
\]
So, \((0, -10)\), \((2, -4)\), and \((4, 2)\) are specific solutions to the equation \(3x - y = 10\).
### Graphical Representation:
The equation \(3x - y = 10\) represents a straight line when graphed on a coordinate plane. You can plot it by using two points:
1. For \(x = 0\), the point is \((0, -10)\).
2. For \(y = 0\), solve for \(x\):
\[
3x - 0 = 10 \quad \Rightarrow \quad 3x = 10 \quad \Rightarrow \quad x = \frac{10}{3} \quad \Rightarrow \quad \left(\frac{10}{3}, 0\right)
\]
Plot these points \((0, -10)\) and \(\left(\frac{10}{3}, 0\right)\) and draw a line through them. This line represents all the solutions to the equation \(3x - y = 10\).
3x-y=10
1 answer