which of the following is a solution for the ststem y = 3x + 5 and y = 2x + 5 a. (1, 7) b. (5, 0) c. (2, -1) d. ( 0, 5)
To find the solution for the system of equations y = 3x + 5 and y = 2x + 5, we need to find the values of x and y that satisfy both equations.
1. Start by equating the two equations since both expressions are equal to y:
3x + 5 = 2x + 5
2. Simplify the equation by subtracting 2x from both sides:
x + 5 = 5
3. Eliminate the constants from the equation by subtracting 5 from both sides:
x = 0
4. Now that we have x = 0, we can substitute this value into either one of the original equations to find the value of y.
For equation y = 3x + 5:
y = 3(0) + 5
y = 5
Therefore, the solution to the system of equations is (0, 5).
Looking at the options provided:
a. (1, 7) - This does not satisfy either equation.
b. (5, 0) - This does not satisfy either equation.
c. (2, -1) - This does not satisfy the second equation.
d. (0, 5) - This is the solution we found earlier, and it satisfies both equations.
Therefore, the correct solution for the system of equations y = 3x + 5 and y = 2x + 5 is option d, (0, 5).