To find the solution of the system of equations given by:
- \( y = -2x + 8 \)
- \( y = 4x - 10 \)
we need to find the point \((x, y)\) where these two lines intersect. This means we can set the two equations equal to each other since both are equal to \(y\):
\[ -2x + 8 = 4x - 10 \]
Now, let's solve for \(x\):
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Add \(2x\) to both sides: \[ 8 = 6x - 10 \]
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Add \(10\) to both sides: \[ 18 = 6x \]
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Divide by \(6\): \[ x = 3 \]
Next, we can substitute \(x = 3\) back into either of the original equations to find \(y\). We'll use the first equation:
\[ y = -2(3) + 8 \] \[ y = -6 + 8 \] \[ y = 2 \]
So, the solution to the system of equations is:
\[ (x, y) = (3, 2) \]
Thus, the lines intersect at the point \((3, 2)\).