How do you solve the system of equations #-2x - 2y = - 4# and #2x + 3y = 9#?
2 Answers
Determine the point of intersection by using substitution and solving for the variables.
Explanation:
Solving a system of equations imply we find the point of interception.
To do this, we must use substitution to find one variable, and use that value to determine the exact value of the other.
Here, we'll isolate
#-2x-2y=-4#
#-2x=2y-4#
#x=-y+2#
Now that we have our variable expression, we can sub this into the other equation and solve for
#2x+3y=9#
#2(-y+2)+3y=9#
#-2y+4+3y=9#
#4+y=9#
#y=5#
Now that we know our
#x=-y+2#
#x=-(5)+2#
#x=-5+2#
#x=~3#
Thus, our point of intersection is
If we graph the two equations, we can see the point of intersection is in fact
graph{(-2x-2y+4)(2x+3y-9)=0 [-8.875, 11.125, -0.36, 9.64]}
Hope this helps :)
Refer to the explanation.
Explanation:
Solve system:
Equation 1:
Equation 2:
Both equations are linear equations in standard form:
The resulting point
The system of equations will be solved using substitution.
Solve Equation 1 for
Add
Divide both sides by
Solve Equation 2 for
Substitute
Simplify.
Subtract
Simplify.
Substitute
Simplify.
Add
Simplify.
Divide both sides by
Simplify.
Point of Intersection: