- the sum of two numbers is 52. the difference of the two numbers is 38. what are the two numbers? so to solve this problem, we're going to set up a system of equations
compare phone plans, and then solve the system. the first thing to notice is we have two numbers, so let's let x = the first number. and we'll let y = the second number.
so the first sentence tells us the sum of the two numbers is 52, and sum means addition. so the first equation will be x + y = 52. next, we're told the difference of the two numbers is 38, and difference means subtraction, so x - y = 38. so here's our system of equations. we'll call this equation 1, and we'll call this equation 2. we're going to go ahead and solve this algebraically
which means we can use either the substitution method to solve this system, or we can use the elimination method to solve the system. in this video, we're going to use the substitution method. in the next video, we'll take a look at the same problem and use the elimination method. so to solve this using the substitution method, we need to select one of the equations and solve it for one of the variables.
for example, if we use equation two, and we solve this for x, we start with x - y = 38. we would add y to both sides,so this tells us x = 38 + y. and now we're going to perform substitution in equation one since x = 38 + y, we'll substitute 38 + y for x into equation 1. so now using equation one, we're going to have 38 + y + y = 52. and now we'll solve this equation for y, so we have 38 + 2y = 52.
so we'll subtract 38 on both sides, so we have 2y = 52 - 38 = 14. divide both sides by 2, and we have y = 7. remember, our goal is to find the 2 numbers. y is the second number, so we know y = 7. but we still have to determine the value of x. so now we can substitute 7 for y into equation one or equation two to determine the value of x, or we have this equation here that says x = 38 + y,
so if y = 7, x = 38 + 7 = 45. so the two numbers that have a sum of 52 and a difference of 38 are 45 and 7. รข
