Is (5,−1) a solution to the system of these linear equations: x+y=4 and 2x+3y=7 ? Why?(1 point)
To determine if (5, -1) is a solution to the system of linear equations, we can substitute the values of x and y into both equations and see if they both hold true.
For the equation x+y=4:
5 + (-1) = 4
4 = 4
Since the equation holds true, (5, -1) is a solution to the first equation.
For the equation 2x + 3y = 7:
2(5) + 3(-1) = 7
10 - 3 = 7
7 = 7
Since the equation holds true, (5, -1) is a solution to the second equation.
Therefore, (5, -1) is a solution to the system of linear equations.
To determine if the point (5, -1) is a solution to the system of linear equations x+y=4 and 2x+3y=7, we can substitute the point's x and y values into both equations and check if both equations are satisfied.
1. Substituting x=5 and y=-1 into the first equation:
5 + (-1) = 4
4 = 4
2. Substituting x=5 and y=-1 into the second equation:
2(5) + 3(-1) = 7
10 - 3 = 7
7 = 7
Both equations are satisfied when substituting the values x=5 and y=-1 from the point (5, -1). Therefore, (5, -1) is indeed a solution to the given system of linear equations.
To determine if the point (5,-1) is a solution to the system of linear equations x+y=4 and 2x+3y=7, we need to substitute the values of x and y from the point (5,-1) into both equations and check if the equality holds true.
Let's substitute x=5 and y=-1 into the first equation:
x + y = 4
5 + (-1) = 4
4 = 4
The equation holds true.
Now, let's substitute x=5 and y=-1 into the second equation:
2x + 3y = 7
2(5) + 3(-1) = 7
10 - 3 = 7
7 = 7
Again, the equation holds true.
Since both equations hold true when we substitute the values x=5 and y=-1, we can conclude that the point (5,-1) is indeed a solution to the given system of linear equations.