To solve the system of equations by substitution, we start with the given set of equations:
1. [tex]\( y = -2x + 30 \)[/tex]
2. [tex]\( y = 0.4x \)[/tex]
Step 1: Set the equations equal to each other since both are equal to [tex]\( y \)[/tex]:
[tex]\[ -2x + 30 = 0.4x \][/tex]
Step 2: Solve for [tex]\( x \)[/tex]. To do this, we need to get all the [tex]\( x \)[/tex] terms on one side and the constants on the other side. Start by adding [tex]\( 2x \)[/tex] to both sides:
[tex]\[ 30 = 2.4x \][/tex]
Step 3: Isolate [tex]\( x \)[/tex] by dividing both sides by 2.4:
[tex]\[ x = \frac{30}{2.4} \][/tex]
[tex]\[ x = 12.5 \][/tex]
So, [tex]\( x = 12.5 \)[/tex].
Step 4: Substitute the value of [tex]\( x \)[/tex] back into one of the original equations to find [tex]\( y \)[/tex]. Let's use the second equation [tex]\( y = 0.4x \)[/tex]:
[tex]\[ y = 0.4 \cdot 12.5 \][/tex]
[tex]\[ y = 5 \][/tex]
Therefore, the solution to the system of equations is:
[tex]\[ x = 12.5 \][/tex]
[tex]\[ y = 5 \][/tex]
So, the ordered pair that solves the system of equations is [tex]\( (12.5, 5) \)[/tex].
