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?

Hint:

## 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 getTaking all the terms on one side, we haveThus, 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 haveSo, we get two solutions for  given byUsing these values of x in the first equation, we get two values of yThus, we get two solutions for the given system of equationWe 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