Ms. Sue
answered
2x + 3y = 101
x = 39 - y
2(39 - y) + 3y = 101
78 - 2y + 3y = 101
y = 23
Take it from there.
Step-by-Step Bot
answered
According to the given information:
1) The sum of two numbers is 39: x + y = 39
2) Twice the first number plus three times the second number is 101: 2x + 3y = 101
We can solve these equations by using the method of substitution or elimination.
Let's solve by the method of substitution:
1) Rearrange the first equation for x:
x = 39 - y
2) Substitute the value of x in the second equation:
2(39 - y) + 3y = 101
Simplify the equation:
78 - 2y + 3y = 101
y + 78 = 101
Subtract 78 from both sides:
y = 101 - 78
y = 23
3) Substitute the value of y in the first equation:
x + 23 = 39
Subtract 23 from both sides:
x = 39 - 23
x = 16
Therefore, the first number is 16, and the second number is 23.
Explain Bot
answered
1. The sum of the two numbers is 39:
This can be represented by the equation: x + y = 39.
2. Twice the first number plus three times the second number is 101:
This can be represented by the equation: 2x + 3y = 101.
We now have a system of two linear equations with two variables. To solve this system, we can use the method of substitution or elimination. I will explain how to solve it using the method of substitution.
1. Solve the first equation (x + y = 39) for one variable:
We can solve for x by subtracting y from both sides of the equation:
x = 39 - y.
2. Substitute the expression for x in the second equation:
Instead of x, we'll write (39 - y) in the second equation:
2(39 - y) + 3y = 101.
3. Simplify the equation:
Distribute the 2:
78 - 2y + 3y = 101.
Combine like terms:
y + 78 = 101.
Subtract 78 from both sides:
y = 101 - 78 = 23.
4. Substitute the value of y back into the first equation to solve for x:
x + 23 = 39.
Subtract 23 from both sides:
x = 39 - 23 = 16.
Therefore, the two numbers are x = 16 and y = 23.
