Determine the number of solutions to the system of linear equations. Y= x + 5
Y= x + 5
7 answers
In this case, the two equations are identical, which means that they represent the same line. Since the lines are the same, the system of equations has infinitely many solutions. The solutions will be all the points on the line defined by y = x + 5.
But what is the answer
The system of linear equations given as Y = x + 5 and Y = x + 5 has infinitely many solutions.
Solving the system y = -x + 3 and x + y = 8 by graphing shows that there is no solution to the system. Is this statement true or false? Explain.
The statement is false.
To solve the system of equations y = -x + 3 and x + y = 8 by graphing, we first rewrite the second equation in slope-intercept form:
x + y = 8
y = -x + 8
Now we can graph both equations:
Equation 1: y = -x + 3
Equation 2: y = -x + 8
When we graph these lines, we find that they intersect at the point (5, -2), which means that there is a single solution to the system of equations. Therefore, the statement that there is no solution to the system is false.
To solve the system of equations y = -x + 3 and x + y = 8 by graphing, we first rewrite the second equation in slope-intercept form:
x + y = 8
y = -x + 8
Now we can graph both equations:
Equation 1: y = -x + 3
Equation 2: y = -x + 8
When we graph these lines, we find that they intersect at the point (5, -2), which means that there is a single solution to the system of equations. Therefore, the statement that there is no solution to the system is false.
Does the graph show the system of equations X + Y = 2 and
-x + y = 7? Should the lines for the system be parallel?
-x + y = 7? Should the lines for the system be parallel?
When we look at the system of equations x + y = 2 and -x + y = 7, we can rewrite the equations in slope-intercept form to determine their graph:
x + y = 2
y = -x + 2
-x + y = 7
y = x + 7
After rewriting the equations, we see that the slopes of the lines are different, which means the lines will not be parallel when graphed. The graph will show two lines that intersect at a point (5, -3), indicating that there is a unique solution to the system of equations.
x + y = 2
y = -x + 2
-x + y = 7
y = x + 7
After rewriting the equations, we see that the slopes of the lines are different, which means the lines will not be parallel when graphed. The graph will show two lines that intersect at a point (5, -3), indicating that there is a unique solution to the system of equations.
2 answers