The two solutions for the system of equations:
y = x^2+ 5x - 3
y - x = 2
Are:
(-5, -7) and (1, -1)
<h3>How to solve the system of equations?</h3>Here we have the following system of equations:
y = x^2+ 5x - 3
y - x = 2
We can replace the first equation into the second one to get:
(x^2+ 5x - 3) - x = 2
x^2 + 4x - 3 = 2
x^2 + 4x - 3 - 2 = 0
x^2 + 4x - 5 = 0
Using the quadratic formula, we will get the solutions:
The two solutions are:
x = (-4 - 6)/2 = -5
x = (-4 + 6)/2 = 1
To find the values of y, we can evaluate the linear equation:
when x = -5
y - (-5) = -2
y + 5 = -2
y = -2 - 5 = -7
So one solution is (-5, -7)
when x = 1
y - 1 = -2
y = -2 + 1 = -1
The other solution is (1, -1)
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