To solve the system of equations
[tex]\[
\begin{array}{l}
y = -2x + 28 \\
y = 0.5x
\end{array}
\][/tex]
by substitution, follow these steps:
### Step 1: Set the two expressions for [tex]\( y \)[/tex] equal to each other
Since both equations equal [tex]\( y \)[/tex], we can set them equal to each other:
[tex]\[
-2x + 28 = 0.5x
\][/tex]
### Step 2: Solve for [tex]\( x \)[/tex]
Combine like terms to isolate [tex]\( x \)[/tex]:
[tex]\[
-2x - 0.5x = -28
\][/tex]
This simplifies to:
[tex]\[
-2.5x = -28
\][/tex]
Now, divide both sides by [tex]\(-2.5\)[/tex]:
[tex]\[
x = \frac{-28}{-2.5}
\][/tex]
Simplify the fraction:
[tex]\[
x = 11.2
\][/tex]
### Step 3: Solve for [tex]\( y \)[/tex]
Substitute the value of [tex]\( x \)[/tex] back into either of the original equations to find [tex]\( y \)[/tex]. We will use [tex]\( y = 0.5x \)[/tex]:
[tex]\[
y = 0.5 \times 11.2
\][/tex]
This simplifies to:
[tex]\[
y = 5.6
\][/tex]
### Summary
The solution to the system of equations is:
[tex]\[
x = 11.2, \quad y = 5.6
\][/tex]
Therefore, the coordinates of the intersection point of these two lines are [tex]\( (11.2, 5.6) \)[/tex].
