Mrspi
Advanced Member
USA
998 Posts 
Posted  09/24/2007 : 18:18:33

quote: Originally posted by Kimberly
Please solve step by step with substitution" 7x4y=2
5x+3Y=22
Personally, I would NOT use substitution to solve this system. Why? Because you can't solve one of the equations for one of the variables without introducing fractions. This would be much easier to solve using the "additionelimination" method.
But...since you asked....
Let's take the first equation, and solve it for y: 7x  4y = 2 Add 7x to both sides: 4y = 7x + 2 Divide both sides by 4: y = (7/4)x  (1/2)
Now, substitute (7/4 x  1/2) for y in the second equation:
5x + 3y = 22
5x + 3(7/4 x  1/2) = 22 5x + (21/4)x  (3/2) = 22
Ok....let's get rid of the fractions. Multiply both sides of the equation by the common denominator for the fractions, which is 4:
4*5x + 4*(21/4)x  4*(3/2) = 4*(22)
20x + 21x  6 = 88 41x  6 = 88 41x = 82 x = 2
And now that we know the value of x, we can find y. y = (21/4)x  (1/2) y = (21/4)*2  (1/2) y = 21/2  (1/2) y = 22/2 y = 11
The last step should always be to CHECK your answer. Are both of the original equations true when x = 2 and y = 11? I'll leave the check to you. 

