Question

The perimeter of a rectangle is 50 cm and the length is 4 cm longer than the width. Write and solve the system of equations using the substitution method.

Answer 1

We know two things from this: that the perimeter is 50 cm and that the length is 4 cm longer than the width.
Our equation will be in terms of the width, since we know that the length is dependent on that.
2(4+w) + 2w=50
Now, we need w to be by itself on one side. We need to distribute the parenthesis and solve.
8+2w+2w=50
8+4w=50
4w=42
w=10.5
Let's check if the width is 10.5 cm with the length being 14.5 cm by adding.
21+29= 50
Now, we know the answer, let's use the substution method. You could substitute many things.
2l+2w=50
2(w+4)=l
By putting the second equation where the L is in the first equation, we would be using substitution. For this problem, they are many ways to substitute and solve the system of equations.