Answer:
7 and 8
Step-by-step explanation:
Let x = the first number
Let y = the second number
First number plus twice a second number is 23: x + 2y = 23
Twice the first number plus the second totals 22: 2x + y = 22
Equation 1: x + 2y = 23
Equation 2: 2x + y = 22
Rewrite equation 1 to make x the subject:
x = 23 - 2y
Substitute into equation 2 and solve for y:
⇒ 2(23 - 2y) + y = 22
⇒ 46 - 4y + y = 22
⇒ -3y = -24
⇒ y = 8
Substitute found value for y into one of the equations and solve for x:
⇒ 2x + 8 = 22
⇒ 2x = 14
⇒ x = 7
Therefore, the two numbers are 7 and 8
