Is (5,−1) a solution to the system of these linear equations: x+y=4 and 2x+3y=7 ? Why?(1 point)
Responses
Yes, because the graphs intersect at (5,−1).
Yes, because the graphs intersect at left parenthesis 5 comma negative 1 right parenthesis .
Yes, because the graphs don’t intersect at (5,−1).
Yes, because the graphs don’t intersect at left parenthesis 5 comma negative 1 right parenthesis .
No, because the graphs don’t intersect at (5,−1).
No, because the graphs don’t intersect at left parenthesis 5 comma negative 1 right parenthesis .
No, because the graphs intersect at (5,−1).
No, because the graphs intersect at left parenthesis 5 comma negative 1 right parenthesis .
To determine if the point (5,-1) is a solution to the system of linear equations, we need to substitute the x and y values into each equation and see if the equations are true.
For the first equation, x + y = 4:
Substituting x=5 and y=-1:
5 + (-1) = 4
4 = 4
For the second equation, 2x + 3y = 7:
Substituting x=5 and y=-1:
2(5) + 3(-1) = 7
10 - 3 = 7
7 = 7
Since both equations are true when the values (x=5, y=-1) are substituted, we can conclude that (5,-1) is a solution to the system of linear equations.
Therefore, the correct answer is:
Yes, because the graphs intersect at (5,-1).