If we graphed them both, this is what we'd end up with:Īs you can see, both lines intersect at the coordinate #(3,6)#. For example, considering the following equations: If there is one solution, it means that there is a single intersection between the two lines that your equations give. With linear systems of equations, there are three possible outcomes in terms of number of solutions: Find the real values of #x# and #y# that satisfy the following systems of equations.Ĭ) #2x^2 - 3y^2 = -10, x^2 - 2x + 3y = 5#.Use the following practice exercises to develop your comfort with the skills dealt with in this answer. This will give you real roots of #2# and #-2#. It looks easiest to isolate the #y# in the first equation, however solving this equation won't be as neat as solving the previous one. Once again, as with the last example, we need to solve for one of the variables in one of the equations.
This is found by inserting #x = 1# into one of the equations and solving for #y#.Įxample 2: Find all real values of #x# and #y# that satisfy the following system of equations: #3y = -2x^2 + 2, 2x^2 - 3y^2 = -4# We can now substitute into the other equation: I think it would be easiest to solve for #y# in the first equation.
Since we want to solve with substitution, we must solve for one variable in one of the equations. So, I've prepared a couple of problems that I will work through slowly and carefully, showing all the steps to the final answer.Įxample 1: Solve the following system of equations- #2x + y = 5, 3x + 2y = 9# I'm not sure where exactly you mean "final" in the solving process.