Find the answer to each instruction and compare them all.
Different: Solve each equation for y.
ly=2x+2 y=4x+6
(-2,-2)
Practice makes perfect
Let's look at each instruction individually and then compare our answers.
Solve the system of linear equations.
We are first asked to solve the system of linear equations. We can do this by solving each equation for y, graphing them both, and finding their point of intersection. The given equations are:
l-4x+2y=4 4x-y=-6
Let's solve the first equation for y so that we can easily graph it using the slope-intercept form.
Next, we can use the slope-intercept form to graph the equations and find their point of intersection.
This graph shows us that the point (-2,-2) lies on both lines and solves the system of equations.
Solve each equation for y.
To solve each equation for y, we simply need to rewrite each equation into slope-intercept form using a series of inverse operations. Let's begin with the first equation.
When we solve each equation for y, we get:
ly=2x+2 y=4x+6.
Find the point of intersection.
To find the point of intersection of the graphs of the equations, we need to first rewrite the equations into slope-intercept form. As we have previously shown, the equations in slope-intercept form are:
&-4x+2y=4 & ⇒ y=2x+2
&4x-y=-6 & ⇒ y=4x+6
We then graph those lines and find where they intersect.
The point of intersection is (-2,-2).
Find an ordered pair that is a solution.
To find an ordered pair that is a solution of each equation in the system, we need to graph the lines and find the point that lies on both lies, their point of intersection. As shown previously, the lines written in slope-intercept form are:
-4x+2y=4 & ⇒ y=2x+2
4x-y=-6 & ⇒ y=4x+6
We then graph those lines and find a point that lies on both lines.
The only ordered pair that lies on both lines is (-2,-2), which is also their point of intersection.
Conclusion
As shown above, when asked to solve a system of equations, find the point of intersection, or find an ordered pair that solves both equations, all give the same result. The point of intersection is the only point that lies on both lines and it, subsequently, solves the system of equations.
(-2, -2)
Being asked to solve for y in each equation is a different question that is often a vital step in the process of solving the system of equations.
ly=2x+2 y=4x+6
