Equation M: y = 3x + 4
Equation P: y = 3x + 7
Which of the following options is true about the solution to the given set of equations?
No solution
One solution
Two solutions
Ininite solutions
I thought it was infinite solutions but i got the answer wrong.
for two lines of the form
y=mx+b
to have infinitely many solutions, they must be the same line. That is, m and b must be the same.
Your two lines are parallel, so they never meet; no solutions.
Equation S: y = x + 9
Equation T: y = 2x + 1
Which of the following steps can be used to find the solution to the set of equations?
x = 2x + 1
x + 9 = 2x
x + 1 = 2x + 9
x + 9 = 2x + 1
To determine the solution to the given set of equations, we need to see if they intersect at any point. We can do this by comparing the coefficients of x and the constants in the two equations.
Equation M: y = 3x + 4
Equation P: y = 3x + 7
Since both equations have the same slope of 3 (the coefficient of x), we can conclude that the lines are parallel and will never intersect. This means that there is no solution to the given set of equations.
Therefore, the correct answer is: No solution.
To determine the number of solutions for a system of linear equations, you need to compare the slopes and y-intercepts of the equations given.
In the given equations:
Equation M: y = 3x + 4
Equation P: y = 3x + 7
Both equations have the same slope (3), but different y-intercepts (4 and 7).
If the slopes are the same and the y-intercepts are also the same, the two equations represent the same line, which means there are infinitely many solutions.
However, if the slopes are the same but the y-intercepts are different, then the two equations represent parallel lines, and there is no point of intersection, resulting in no solution.
In this case, we have the same slope (3) but different y-intercepts (4 and 7), which means the equations represent parallel lines and have no point of intersection. Therefore, the correct answer is "No solution."