System of Equations: 2x+y=10 & (I) 2x+3y=22 & (II) Time to Jog around the Park: 6 minutes
Practice makes perfect
We want to determine how long it takes for us to jog around the park. Let's use the information from the exercise to create a system of linear equations and then solve it using the Elimination Method. We will use x to represent the time we need to jog around the block and y to represent the time we need to jog around the park.
Time to Jog Around the Block - x Time to Jog Around the Park - y
From the exercise we know that we can jog around our block twice and the park once in 10 minutes. Let's write this fact as an equation.
2* x+ 1* y= 10 ⇕ 2* x+ y= 10
We also know that it takes us 22 minutes to jog around the block twice and 3 times around the park.
2* x+ 3* y= 22
Now that we have created two equations, we can combine them into a system of equations. Let's take a look.
2x+y=10 & (I) 2x+3y=22 & (II)
We are ready to solve this system to find how long it takes us to jog around the park. This means we want to eliminate the x-variable since it represents the amount of time it takes to jog around the block. Let's subtract Equation (I) from Equation (II) to get an equation in only one variable, y.
