Answer x = 12 and y = 9 Step by step First identify the equations The sum of two numbers is 21 x + y = 21 Change to y intercept for ease of math y = 21 - x ( call this equation a) Three times the larger is equal to four times the smaller 3x = 4y (call this equation b) Now substitute the value of y = 21 -x into equation b 3x = 4(21-x) Distribute 3x = 84 - 4x Now we want to isolate x by adding 4x to each side 3x + 4x = 84 -4x + 4x Combine like terms 7x = 84 Now solve for x by dividing both sides by 7 x = 12
Now to find y Using equation a from above y = 21 - x Substitute our x value of 12 into equation y = 21 - 12 solve for y y = 9 Now check your work x = 12 and y = 9 The sum of two numbers is 21 12 + 9 = 21
Three times the larger (x) is equal to four times the smaller (y) 3x12 = 4x9 36 = 36 Problem solved!!
