Maths-
General
Easy
Question
The system of equations above is graphed in the xy -plane. At which of the following points do the graphs of the equations intersect?
- ( - 3, - 2 )
- ( - 3, 2 )
- ( 5, - 2 )
- (5, 14 )
Hint:
Hint:
The given two equations are graphed on the xy plane. Obviously, every point on the curve will satisfy the equation. The point at which the lines intersect will satisfy both the given equations. Such a point will be the solution of the system of equations. So, we simply need to solve the given system of equations to get the point which intersects the graphs of the equations.
The correct answer is: (5, 14 )
The given equations are:
We will use the method of substitution to solve these equations.
From the first equation, we use the value of in the second equation,
We get an equation in one variable.
Simplifying this, we get
Taking all the terms on one side, we have
Thus, we get a quadratic equation,
factorization to solve We use middle term the above equation.
factorization to solve We use middle term the above equation.
Now, taking common from the first two terms and 2 from the last two terms, we have
So, we get two solutions for given by
Using these values of x in the first equation, we get two values of y
Thus, we get two solutions for the given system of equation
We can see that ( 5, 14 ) is in the options.
The correct option is D).
Note:
We can solve the equations by other methods too, but the method of substitution is most suitable here. Also, instead of solving
by middle term factorisation, we could also use the quadratic formula, which is given by
Where the standard form of equation is 
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