# Tutor profile: Rebecca B.

## Questions

### Subject: Pre-Algebra

Describe three ways to solve a system of equations.

One way to solve a system of equations is by graphing. You can graph the two equations and see its point of intersection. This would be the solution. Another way to solve a system of equations is by substitution. You can solve one of the equations for x or y and then substitute that into the other equation. Once you solve for one of the variables, you can substitute that number into one of the equations to get the other variable. A third way is by elimination. You can rewrite one or both equations so that one of the variables cancels out. Once they cancel out, you can solve for the other variable. Similar to substitution, once you have the value of one of the variables, you can plug it into one of the equations and solve for the other variable.

### Subject: Basic Math

Simplify the fraction: 6/8

Since 6 and 8 can both be divided by the same number, it can be simplified. You want to find the largest number that goes into 6 and 8, which is 2. When you divide both numbers by 2, you get 3/4. This is equivalent to 6/8.

### Subject: Algebra

Factor the polynomial: x^2 + 4x - 60

To solve this polynomial, you first want to see if there is a greatest common factor (GCF) to factor out. Since there is not a GCF, you want to find two numbers that multiply to -60 and add to 4. You can list all of the factors to see which pair adds to 4 (1 & -60, -1 & 60, 2 & -30, -2 & 30, 3 & -20, -3 & 20, 4 & -15, -4 & 15, 5 & -12, -5 & 12, 6 & -10, -6 & 10). The pair that works is -6 and 10. Since you know these two numbers multiply to -60 and add to 4, you want to rewrite them as two binomials. This would be (x-6)(x+10). You can check your answer by multiplying the binomials to see if you get your original polynomial.