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Solving Linear-Quadratic Systems

Solving Linear-Quadratic Systems 1.11 - Solution

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We want to solve the given system of equations using the substitution method. The -variable is isolated in Equation (II). This allows us to substitute its value for in Equation (I).
Notice that in Equation (I), we have a quadratic equation in terms of only the -variable. Now, recall the Quadratic Formula. We can substitute and into this formula to solve the quadratic equation.
Solve for
Since adding or subtracting zero doesn't change the value of a number, the numerator will simplify to Therefore, we will get only one value of Now, consider Equation (II). We can substitute into the above equation to find the value for
We found that when The solution of the system, which is a point of intersection of the parabola and the line, is