Determine whether the point(7,2) is a solution of the system..-3x+4y=-13,-2x+8y=2,by substituting the point into each equation.
To determine if the point (7,2) is a solution to the system, we need to substitute the values of x and y into each equation of the system and check if both equations are true.
Let's start with the first equation, -3x + 4y = -13. Substituting x = 7 and y = 2 into the equation, we get:
-3(7) + 4(2) = -13
-21 + 8 = -13
-13 = -13
Since -13 = -13, the first equation is true when substituting (7,2).
Now let's move onto the second equation, -2x + 8y = 2. Substituting x = 7 and y = 2 into the equation, we get:
-2(7) + 8(2) = 2
-14 + 16 = 2
2 = 2
Again, since 2 = 2, the second equation is also true when substituting (7,2).
Therefore, the point (7,2) is a solution to the system because it satisfies both equations.