# Video: Writing and Solving Two-Step Linear Equations in a Geometric Context

Find the value of 𝑎 given the following information: 𝑌 is on the line between 𝑋 and 𝑍. 𝑋𝑌 = 24 cm. 𝑌𝑍 = 8𝑎 cm. 𝑋𝑍 = 88 cm.

01:53

### Video Transcript

Find the value of 𝑎 given the following information: 𝑌 is on the line between 𝑋 and 𝑍. 𝑋𝑌 equals 24 centimeters, 𝑌𝑍 equals eight 𝑎 centimeters, and 𝑋𝑍 equals 88 centimeters.

We can begin this question by drawing the line 𝑋𝑍 on which 𝑌 lies. We’re told that 𝑋𝑌 equals 24 centimeters, 𝑌𝑍 equals eight 𝑎 centimeters, and the length of the whole line 𝑋𝑍 is 88 centimeters. The length from 𝑋𝑌 plus the length from 𝑌𝑍 is equal to the total distance from 𝑋 to 𝑍. As all of our measurements are in centimeters, this can be written as an equation. 24 plus eight 𝑎 is equal to 88. We can then solve this equation to calculate the value of 𝑎. We begin by subtracting 24 from both sides. As 88 minus 24 is equal to 64, we have eight 𝑎 equals 64. We can then divide both sides of this new equation by eight. This gives us the value of 𝑎 equal to eight.

We can check this by substituting this value back in. From the line above, we actually know that eight 𝑎 is equal to 64. This means that the length of the line from 𝑌 to 𝑍 is 64 centimeters. As 24 centimeters plus 64 centimeters equals 88 centimeters, our answer is correct.