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module 5

system of equations

How many linear equations are in a system of equations? Answer: Two or more
Is an ordered pair of numbers a solution of the system of two equations? Answer: Yes
How do you determine if (12,6)an ordered pair, is a solution to the system of equations 2x-3y=6 and x=2y? Replace x with 12 and y with 6 in both equations. solve the equations. If the solutions are true statements than the ordered pair is a solution of the system.
solve the following equations to see if (12,6)is a solution to the following system. 2x-3y=6 and x=2y 2x-3y=6 2(12)-3(6)=6 replace x with 12 and y with 6 24-18=6 solve 6=6 True x=2y Replace x with 12 and y with 6 12=2(6) solve 12=12 True
If an ordered pair is a solution to the system of equations, does the ordered pair have a common point to the graphs of both equations? Yes, The ordered pair will also have a common point on the graphs of the equations.
The point of intersection gives the solution of the system. How many solutions are there to the system? Only one solution to the system if the lines of the graph intersect at a point.
If you have two equations of a system without a given ordered pair, how do you solve? You need to make a matrix solving for both x and y in order to find the ordered pairs.
Once you solve for x and y in the equations how do you graph the solution of the system? Take two ordered pairs from the matrix and graph the lines. The intersecting point of the lines is the solution to the system.
How do you solve a system of linear equations without graphing? Each equation must first be written in slope-intercept form (y=mx+b)Then solve the equations.
Solve for the following system of equations without graphing. 9x+y=4 and -x+7y=-49 Write both in slope-intercept form y=-9x+4 and 7y=x-49 Then solve for y y=1/7x-7 the two equations are y=-9x +4 and y=1/7x-7
In the equations y=-9x+4 and y=1/7x-7 how many solutions to the system? There is only one solution since the slopes and the y-intercepts are different. This tells us that the equations are lines intersecting at a single point which can have only one solution
In the equations y=1/2x-2 and y=1/2x-5/2 how many solutions to the system if the slopes are the same? There is no solution to the system, since the slopes are the same and the y-intercept is different this tells us that the lines are parallel.
In the equations y-3x=2 and -6x+2y=4 how many solutions to the system? put the equations in slope-intercept form which are y=3x+2 and 2y=6x+y(solve for y) This gives the equation y=3x+2 since the slope and y-intercept are the same in both equations the lines of the graph are identical, there are infinitely many solutions.
Solving linear equations by substitution is more accurate than graphing the solution? Yes, especially if fractions are involved which are hard to graph accurately.
What is the first step to solving a linear equation by substitution? First you need an equation solved for one of its variables either x or y, If neither equation is solved for x or y, this will be your first step.
Solve for x in the linear equation x+2y=7 of the equations in the system of x+2y=7 and 2x+2y=13 solve for x by getting the x variable on the left side of the equation by itself. Do this by subtracting 2y from both sides of the equation. The answer is x=7-2y
What is the second step to solving the system of x+2y=7 and 2x+2y=13 by substitution? You solved for x which is x=7-2y Second step is to substitute x with 7-2y in the second equation of 2x+2y=13. The answer is y= 1/2
What is the third step to solving the system of x+2y=7 and 2x+2y=13 by substitution? The third step is solving for x. You substitute y=1/2 in the equation x=7-2y. x=7-2(1/2) which equals x=6 you now have the ordered pair (6,1/2) which is the solution to the system of equations of x+2y=7 and 2x+2y=13
If solving a linear equation with substitution and one of the variables is already solved such as x=y+2, do I have to solve for one of the variable's as the first step? No, simply substitute the x variable with y+2 in the other equation.
How do I check to see if my solutions are correct? by replacing the ordered pair into the two original equations.
Created by: cleann