# Tutor profile: Rebecca W.

## Questions

### Subject: Pre-Algebra

Combine Like terms: 2x +7y + 3x + 2y

Step 1) reorganize the equation so like variables are next to each other: 2x + 3x + 7y + 2y Step 2: Combine like terms: x + x + x + x + x + y + y + y + y + y + y + y + y + y 5x + 2y

### Subject: Basic Math

Add the fractions by finding a common denominator: 1/4 + 2/6

Step 1) Find the least common multiple of 4 and 6. Multiples of 4: 4, 8, 12, 16, 20 Multiples of 6: 6, 12, 18, 24 The least common multiple is 12. Step 2) Multiply 1/4 by 3/3 to get the denominator of 12. 1/4 x 3/3 = 3/12 Step 2) Multiply 2/6 by 2/2 to get the denominator of 12. 2/6 x 2/2 = 4/12 *NOTICE: we are not changing the the original fractions by multiplying them by 2/2 or 3/3. When you multiply ANY number by 1, the answer is that same number. Ex: 3 x 1 = 3, or 1000 x 1 = 1000. Since 3 divided by 3 (or 3/3) is 1, and 2 divided by 2 (or 2/2) is 1, we are simply multiplying both fractions by 1 in a unique way in order to find a common denominator. Step 3) Once you have a common denominator, add the fractions. 3/12 + 4/12 = 7/12. *Remember, when adding fractions you only add the numerators!

### Subject: Algebra

Solve the system of equations using the substitution method. 2x + 3y = 12 x + y = 5

Step 1) Choose an equation and solve for one variable. Let's choose the 2nd equation, and solve for x. x + y = 5 *subtract y from both sides -y -y x= 5 - y Step 2) Plug the new value of x (which is 5-y) into the first equation to solve for y. 2 (5 - y) + 3y = 12 *use the distributive property to "undo" the parentheses. 10 - 2y + 3y = 12 *combine your ys by adding -2 y + 3y, or 3y - 2y, which = 1y 10 + y = 12 *subtract 10 from both sides -10 -10 y=2 Step 3) Plug y= 2 into either equation to solve for x. x + 2 = 5 *subtract 2 from both sides - 2 -2 x= 3 Answer: The solution to the equation is x= 3 and y = 2, or (3,2) Step 4: Plug the x and y values into both equations to check your answer. x + y = 5 3 + 2 = 5 ---> correct! 2x + 3y = 12 2(3) + 3(2) = 12 6 + 6 = 12 ---> correct!

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