Question

What is the solution to the system of equations?-3x + 5y = 10y = -2x + 15(a) Use the substitution method to find the solution.(b) What do you know about the two lines in this system of equations (Hint: Do they intersect? Are theyparallel? Are they the same line?)

Answer 1

a. Use the second equation, that expresses y in terms of x, to replace y in the first equation:

`\begin{gathered} -3x+5(-2x+15)=10 \\ -3x-10x+75=10 \\ -13x+75=10 \\ -13x=10-75 \\ -13x=-65 \\ x=(-65)/(-13) \\ x=5 \end{gathered}`

Use the value of x to find y:

`\begin{gathered} y=-2(5)+15 \\ y=-10+15 \\ y=5 \end{gathered}`

It means that the solution of this system of equations is (5, 5).

b. From the obtained solution, we can say that these lines intersect at the point (5, 5) (a solution can be interpreted as the intersection of two lines).