Question

Solve the system by substitution. You must show your work.

-2.5x + y = 13.5
2.25x - y = -12.25

Answer 1

x = -4, y = 3.5

Explanation:

-2.5x + y = 13.5 ------ (1)

2.25x - y = -12.25 ---(2)

you can substitute (1) into (2) or vice versa

We are going to substitute (2) into (1)

but first we have to rewrite it in terms of x or y

Lets do y

from (2), (after subtracting -2.25x from both sides), y = 12.25 + 2.25x ----(3)

plug in (3) into (1)

-2.5x + (12.25 + 2.25x) = 13.5

-2.5x + 12.25 + 2.25x = 13.5

-2.5x + 2.25x = 13.5 - 12.5

-0.25x = 1

x = -(1/.25)

x = -4

Now we have x

We already used (2), lets plug in x = -4 into (1)

-2.5(-4) + y = 13.5

10 + y = 13.5

y = 13.5 - 10

y = 3.5

Answer 2

Answer: (-5,1)

Explanation:

−2.5x+y=13.5

−2.5x+y+2.5x=13.5+2.5x(Add 2.5x to both sides)

y=2.5x+13.5

Step: Substitute

5x+13.5 and 2.25x−y=−12.25:

2.25x−y=−12.25

2.25x−(2.5x+13.5)=−12.25

−0.25x−13.5=−12.25(Simplify both sides of the equation)

−0.25x−13.5+13.5=−12.25+13.5(Add 13.5 to both sides)

−0.25x=1.25

−0.25=1.25−0.25(Divide both sides by -0.25)

x=−5

Step: Substitute−5forxiny=2.5x+13.5:

y=2.5x+13.5

y=(2.5)(−5)+13.5

y=1(Simplify both sides of the equation)