Solving Linear Equations with Elimination

What is the primary goal when solving a system of two linear equations?

• To find values that satisfy only one equation

• To find values that satisfy both equations

• To graph the equations

• To eliminate all variables

What happens when you add the equations x - 4y = -18 and -x + 3y = 11?

• Both variables are eliminated

• No variables are eliminated

• y is eliminated, resulting in an equation in x

• x is eliminated, resulting in an equation in y

What is the result of adding -x to x in the equations?

• Eliminates y

• Eliminates x

• None of the above

• Creates a new variable

What is the value of y when the equations are simplified and added?

• 18

• 11

• -7

• 7

What is the equation formed after eliminating x by adding the two given equations?

• -x = -18

• x = 10

• y = 7

• -y = -7

How do you find the value of x after determining y = 7?

• Substitute y = 7 into the first equation

• Substitute y = 7 into the second equation

• Multiply the first equation by 7

• None of the above

After finding y = 7, what is the next step to find x?

• Divide both equations by 7

• Add 7 to both sides of one equation

• Substitute y = 7 in any equation

• Graph the equations

What is the value of x when y = 7 and substituted into the equation x - 4y = -18?

• -18

• -7

• 7

• 10

What does the intersection of the lines on the graph represent?

• A solution that satisfies both equations

• A solution that satisfies neither equation

• A solution that satisfies only one equation

• There is no intersection of lines

How can you verify that x = 10 and y = 7 is the correct solution to the system of equations?

• Graph the equations and check the intersection

• Add 10 and 7

• Multiply both equations by 10

• Substitute x = 10 and y = 7 into both equations