How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent #3x - 2y = 10# and #5x + 2y = 6#?
1 Answer
The lines intersect at a single point, therefore the system of equations is consistent.
Explanation:
Equation 1:
Equation 2 :
Both equations are in the standard form for a linear equation. This form makes it easy to determine the x- and y-intercepts. We can use those two points to graph each equation.
X-intercept: value of
Substitute
Y-intercept: value of
Substitute
Equation 1
X-intercept: Substitute
Divide both sides by
x-intercept:
Y-intercept: Substitute
Divide both sides by
y-intercept:
Draw a straight line through the two points. This is the graph for Equation 1.
Equation 2
X-intercept: Substitute
Divide both sides by
x-intercept:
Y-intercept: Substitute
Divide both sides by
y-intercept:
Draw a line between the two points. This is the graph of Equation 2.
The lines intersect at a single point, therefore the system of equations is consistent.
graph{(3x-2y-10)(5x+2y-6)=0 [-10, 10, -5, 5]}