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y = -2x + 8

y = 4x - 10

Review the graphs of a system of these two linear equations in two variables: y = 4x - 10 and y = -2x + 8 Find the solution of the system.

The solution of the system of
equation is (__).

1 answer

To find the solution of the system of equations given by:

  1. \( y = -2x + 8 \)
  2. \( y = 4x - 10 \)

we can solve for \( x \) by setting the two right-hand sides equal to each other since both expressions equal \( y \):

\[ -2x + 8 = 4x - 10 \]

Now, let's solve for \( x \):

  1. Add \( 2x \) to both sides:

\[ 8 = 6x - 10 \]

  1. Add \( 10 \) to both sides:

\[ 18 = 6x \]

  1. Divide both sides by \( 6 \):

\[ x = 3 \]

Next, we can substitute \( x = 3 \) back into either equation to find \( y \). We'll use the first equation:

\[ y = -2(3) + 8 \]

Calculating this gives:

\[ y = -6 + 8 = 2 \]

Thus, the solution of the system of equations is:

\[ \text{The solution of the system of equations is } (3, 2). \]