To solve the system of equations, we can use the method of substitution.
Step 1: Solve one of the equations for one variable in terms of the other variable.
From the second equation, rearrange as x = Y - 2.
Step 2: Substitute the expression from step 1 into the other equation.
Substituting x = Y - 2 into the first equation gives (Y - 2)² + 5(Y - 2) - 3 = Y² + 5Y - 15.
Step 3: Simplify and solve the resulting equation.
Expanding and simplifying the equation, we get Y² - 9Y + 13 = 0.
Factoring or using the quadratic formula can be used to solve this quadratic equation. In this case, the factors are (Y - 13)(Y + 1) = 0.
So, Y - 13 = 0 or Y + 1 = 0.
If Y - 13 = 0, then Y = 13.
If Y + 1 = 0, then Y = -1.
Step 4: Substitute the values of Y obtained into the expression for x.
When Y = 13, x = Y - 2 = 13 - 2 = 11.
When Y = -1, x = Y - 2 = -1 - 2 = -3.
Therefore, the solutions to the system of equations are x = 11, Y = 13 or x = -3, Y = -1.
Y=x^(2)+5x-3
Y-x=2
Solve the system of equations
1 answer