Topic 2 Simultaneous Equations - Substitution Flashcards
What is the graphical interpretation of simultaneous equations?
The graphical interpretation is the point where the two lines intersect.
In the equations x = 2y and 3y + x = 12, what is the first step?
Substitute x = 2y into 3y + x = 12.
What happens if the lines represented by the simultaneous equations are parallel?
There is no solution, as the lines do not intersect.
What method is used to solve simultaneous equations by substitution?
The substitution method involves solving one equation for one variable and substituting that expression into the other equation.
What is the solution to the simultaneous equations 5x + 3y = 21 and y = 2x?
x = 3, y = 6
True or False: The substitution method can be used for any system of linear equations.
True
True or False: The substitution method can be used to solve non-linear equations.
True
What does it mean to isolate a variable?
To isolate a variable means to manipulate an equation so that the variable is on one side by itself.
If you have the equations x + 2y = 8 and y = 4 - x, what do you do first?
Substitute y = 4 - x into x + 2y = 8.
In the equations y = 2x + 3 and 2x + y = 11, what is the first step in the substitution method?
Substitute the expression for y from the first equation into the second equation.
Which of the following is a necessary condition for using substitution to solve simultaneous equations? a) At least one equation must be linear b) Both equations must be quadratic c) Both equations must have the same variables
a) At least one equation must be linear
What is the first step to solve the equations y = 5x - 3 and 2x + y = 7?
Substitute y = 5x - 3 into 2x + y = 7.
Which variable should you isolate in the equation 2x + 3y = 6 to use substitution?
You can isolate either variable; however, isolating y is common.
Solve for x in the equations x + 3 = 2y and y = x/2 + 1.
x = 0
What is the first step to solve the equations 4x - y = 1 and y = 3x + 2?
Substitute y = 3x + 2 into 4x - y = 1.
What is the solution to the equations 2x + 3y = 6 and 4x + 6y = 12?
There are infinitely many solutions; the equations are dependent.
True or False: The substitution method is always the easiest method for solving simultaneous equations.
False
True or False: The substitution method is less effective than the elimination method.
False
What is the importance of checking your solution after solving simultaneous equations?
To ensure that the solution satisfies both original equations.
In the equations 2y = x + 4 and y = 3x - 2, what do you substitute into?
Substitute y = 3x - 2 into 2y = x + 4.
What is the solution of the simultaneous equations 3x + 2y = 12 and x - y = 1?
x = 2, y = 3
When using substitution, what is the result of substituting x = 5 into the equation y = 2x - 1?
y = 9
Fill in the blank: To solve the equations x + y = 10 and y = 3x, substitute ______ into the first equation.
3x
What is a simultaneous equation?
A simultaneous equation is a set of equations with multiple variables that are solved together.
