Tutor profile: Felicia W.

What is -6 + 18?

Let's go to our number line and make a dot at our first value of -6. This is where we are beginning. Because we are adding a positive, we will move right, in the positive direction on the number line. We start at -6 and move 18 places in the positive direction on the number line. With these moves, we will be at 12. So -6 + 18 = 12. You can also think of this in terms of money. If you owed someone -6 and you had 18 dollars. How many dollars would you have left if you gave the person the 6 dollars you owed them. 18 - 6 = 12. So -6 + 18 = 12.

What would you fill in the blank with to make the equation correct? 3 + ___ = 11

Let's think this way: If we needed 11 oranges ( let's draw our 11 oranges) and we already had 3 oranges ( let's cross out 3 of the 11 oranges that we already have, then how many more oranges do we need to get to the 11 ( count how many oranges remain.) So the blank would be filled in with 8, because we need 8 more oranges from the 3 we already have to get to the 11 oranges we need.

What are the three methods for solving a system of linear equations? Use two of these methods to find the solution to this system of linear equations: y = 3x - 4 4x -4y = 8

The three methods for solving a system of linear equations are graphing, substitution, or elimination. Method 1 : Solving by substitution requires taking the expression that y or x is equal to in one of the equations and substituting that expression for x or y in the second equation. Doing this will allow you to have an equation written in terms of one variable. Once you have an equation written in one variable, you can solve the equation for the value of that variable. Once you know the value of the first variable ( x or y), you will then substitute that value into the first equation to get the value of the second equation. You will then write your solution of the system of linear equations as the point (x, y). Be aware that a system could have no solution if the equations in the system have the same slope or infinitely many solutions if the equations in the system are the identical equation. 4x - 4(3x -4) = 8 4x - 12x + 16 = 8 -8x + 16 = 8 -8x = -8 x = 1 y = 3(1) -4 y = -1 Solution: (1, -1) Method 2: Solving by elimination requires being able to add or subtract the two equations in the system in order to eliminate or get rid of one of the variables so you can solve for the other variable. In order for this to work, you must have opposite value coefficients on one of the variables. If you find a value for the first variable then you will plug that value back into one of the equations to solve for the second variable and then write your solution (x,y). Be aware that a system could have no solution if the equations in the system have the same slope or infinitely many solutions if the equations in the system are identical equations. y = 3x - 4 - rewrite in standard form 4x - 4y = 8 -3x + y = -4 - Multiply this equation by 4 to get opposite value coefficients on y -12x + 4y = -16 No you have a different looking system of equations: 4x -4y = 8 -12x + 4y = -16 Add these two equations together to eliminate y and solve for x -8x = -8 x = 1 Substitute x = 1 into any of the previous equations in the system to get y's value y = 3(1) -4 = -1 Solution: (1,-1)