Point of intersection

Find the point of intersection of the lines with the given equations.
5x + 2y = -11 and 4x + 3y = -6

---

To find the point of intersection of the two lines, solve the two equations
simultaneously for x and y, by either using the addition or substitution method.

Using the addition method:
5x + 2y = -11 -----> -15x - 6y = 33   {multiplied top equation by -3}
4x + 3y = -6 --------> 8x + 6y = -12   {multiplied bottom equation by 2}

-7x = 21   {added the two new equations together}
x = -3   {divided both sides by -7}

5x + 2y = -11   {top equation}
5(-3) + 2y = -11   {substituted -3, in for x, into top equation}
-15 + 2y = -11   {multiplied 5 by -3}
2y = 4   {added 15 to both sides}
y = 2   {divided both sides by 2}

x = -3 and y = 2
(-3,2) is the point of intersection

Ask Algebra House