y=-x+8
x+y=7
a)(1/2,15/2)
b)system has infinitely many solutions
c)(-1/2,17/2)
d)no solutions
y = -x+8 and x+y=7 OR y = -x +7
Line are parallel, both with slopes = -1
y = -x+8
y = -x+7
There is no solution
To solve this system of equations, you can use the method of substitution or elimination. Let's use the method of substitution:
1. First, solve one equation for one variable in terms of the other. Let's solve the second equation for x:
x + y = 7
x = 7 - y
2. Substitute the expression for x into the other equation:
y = -x + 8
y = -(7 - y) + 8
3. Simplify and solve for y:
y = -7 + y + 8
y - y = 8 - 7
0 = 1
4. Since 0 does not equal 1, the equation is inconsistent and has no solutions.
Therefore, the correct answer is (d) no solutions.