Is (5,-1) a solution to the system of these linear equations: x+y=4 and 2x+3y =7? Why?
A. No because the graphs intersect at (5,-1)
B. Yes because the graphs don’t intersect at (5,-1)
C. Yes because the graphs intersect at (5,-1)
D. No because the graphs don’t intersect at (5,-1)
B. Yes because the values of x and y satisfy both equations.
That’s wrong?
Apologies for the confusion. The correct answer is C. Yes because the values of x and y satisfy both equations. The given point (5, -1) satisfies both equations when substituted into them. The left side of each equation will equal the right side when x = 5 and y = -1. Therefore, (5, -1) is a solution to the system of linear equations.
To determine whether (5, -1) is a solution to the system of linear equations x+y=4 and 2x+3y=7, we can substitute the values of x and y into both equations and see if they are satisfied.
For the first equation, x+y=4:
Substituting x=5 and y=-1, we get:
5+(-1)=4
4=4
Since the left side of the equation is equal to the right side (4=4), the point (5, -1) satisfies the first equation.
For the second equation, 2x+3y=7:
Substituting x=5 and y=-1, we get:
2(5)+3(-1)=7
10-3=7
7=7
Again, the left side of the equation is equal to the right side (7=7), so the point (5, -1) satisfies the second equation as well.
Since (5, -1) satisfies both equations in the system, we can conclude that the answer to the question is:
C. Yes because the graphs intersect at (5,-1)