is (-1, 5) a soultion for each system?
x + y = 4
x=-1
can someone please explain how to solve this?
thanks.
Yes, it is.
Put in -1 for x in the first equation, solve for y.
-1 + y = 4
y = 4 + 1
y = 5
To determine if (-1, 5) is a solution for the system, we need to substitute the values of x and y into each equation of the system and see if the equations are true.
1. The first equation is x + y = 4.
- Substitute x = -1 and y = 5 into the equation: (-1) + 5 = 4.
- Simplify: 4 = 4.
Since the equation is true, (-1, 5) is a solution for the first equation.
2. The second equation is x = -1.
- Substitute x = -1: -1 = -1.
Since the equation is true, (-1, 5) is also a solution for the second equation.
Therefore, (-1, 5) is a solution for the given system of equations.
To solve the system, we can follow these steps:
1. For the first equation, x + y = 4, we can solve it for y to get y = 4 - x.
2. Substitute the expression for y in the second equation, which is x = -1.
3. Replace x in the expression for y: y = 4 - (-1) = 4 + 1 = 5.
4. So the solution is (-1, 5).