We want to solve the given system of equations using the Elimination Method.
y=x^2-13x+52 & (I) y=-14x+94 & (II)
By subtracting Equation(II) from Equation (I), we can eliminate the y-variable. Let's do it!
Notice that in Equation (I), we have a quadratic equation in terms of only the x-variable.
x^2+x-42=0 ⇔ 1x^2+ 1x+( - 42)=0We can substitute a= 1, b= 1, and c= - 42 into the Quadratic Formula.
We found that y=10 when x=6. One solution to the system, which is a point of intersection of the parabola and the line, is (6,10). To find the other solution, we will substitute - 7 for x in Equation (II) again.
We found that y=192 when x=- 7. Therefore, our second solution, which is the other point of intersection of the parabola and the line, is (-7,192).
Checking Our Answer
Checking the answer
We can check our answers by substituting the points into both equations. If they produce true statements, our solutions are correct. Let's start by checking (6,10). We will substitute 6 and 10 for x and y, respectively, in Equation (I) and Equation (II).
