Solutions to Linear Equations Solving and Finding Slope

What would be the first step in finding the solution using elimination?

• you cannot solve this using elimination

• cross out the 2x and 3x

• Add the like terms. The y terms will cancel out.

• change to slope intercept form and graph

What is an important step in solving a system by Substitution?

• Make sure both equations are in standard form.

• Make sure at least one equation is solved for one variable.

• Make sure both equations are the same.

• Make sure both equations can be solved.

What would be the first step to solve this system by elimination?

• Add the equations

• Subtract the equations

• Write each equation in slope intercept form.

• Multiple the first equation by 3 or -3

To eliminate the x-variable in the system of equations, multiply the second equation by which number?

• -3

• -2

• -1

• 0

Which strategy is the best choice for solving this system?

4x − 4y = 10

4x + 4y = 0

• Elimination

• Making trials

• Substitution

• Graphing

Which strategy is the best choice for solving this system?

• Elimination

• Elimination with multiplication

• Substitution

• Graphing

Which choice shows substitution correctly?

• 2x + 4(3y - 7) = 9

• 2(3y -7) + 4y = 9

A method for solving a system of equations by replacing one variable with an expression involving the remaining variable(s). For example, in the system of equations above, the first equation tells you that y is equal to –3x + 5. We can substitute –3x + 5 in for y in the second equation to get 2(–3x + 5) + 10x = 18, then solve this equation to find x. Once we have x, we substitute that value back into either of the original equations to find the value of y.

• system of equations

• infinite solutions

• elimination method

• substitution method

A method for solving a system of equations. The key step in using the _________________ is to add both sides of two equations to eliminate one of the variables. For example, the two equations in the system above can be added together to get the simplified result 7x = 14. We can solve this equation to find x, then substitute the x-value back into either of the original equations to find the value of y.

• infinite solutions

• elimination method

• substitution method

• system of equations

The number or numbers that when substituted into an equation or inequality make the equation or inequality true. For example, x = 4 is a ________ to the equation 3x – 2 = 10 because 3x – 2 equals 10 when x = 4. A ________ to a two-variable equation is sometimes written as an ordered pair (x, y). For example, x = 3 and y = –2 is a ________ to the equation y = x – 5; this ________ can be written as (3, –2).

• solution

• no solution

• intersect

• parallel