Determine the number of solutions to this system of linear equations:
y=x+5
y=−x+5 (1 point)
Responses
0
0
1
1
2
2
infinite
The number of solutions to this system of linear equations is 1.
Use the image to answer the question.
A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The equation of the solid line is y equals negative x plus 3. The equation of the dashed line is x plus y equals 8.
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.
(1 point)
Responses
The statement is false, because the lines are parallel.
The statement is false, because the lines are parallel.
The statement is false, because the lines have an intersection point.
The statement is false, because the lines have an intersection point.
The statement is true, because the lines are parallel.
The statement is true, because the lines are parallel.
The statement is true, because the lines have an intersection point.
The statement is true, because the lines have an intersection point.
Use the image to answer the question.
A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The equation of the solid line is y equals negative x plus 3. The equation of the dashed line is x plus y equals 8.
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.
(1 point)
Responses
The statement is false, because the lines are parallel.
The statement is false, because the lines are parallel.
The statement is false, because the lines have an intersection point.
The statement is false, because the lines have an intersection point.
The statement is true, because the lines are parallel.
The statement is true, because the lines are parallel.
The statement is true, because the lines have an intersection point.
To determine the number of solutions to a system of linear equations, you need to analyze the equations. In this case, we have two equations with two variables, x and y.
The given equations are:
1) y = x + 5
2) y = -x + 5
We can solve this system by setting the right sides of the equations equal to each other, since they both equal 5. So, we can write:
x + 5 = -x + 5
If we simplify this equation, we get:
2x = 0
Dividing both sides by 2, we find:
x = 0
Now, we can substitute this value of x back into either of the original equations to find the corresponding value of y. Let's use the first equation:
y = x + 5
y = 0 + 5
y = 5
So, the system of equations has one unique solution: (x, y) = (0, 5).
Therefore, the correct answer is 1 solution.