Graph the equations to solve the system y= 1/2x + 6 y = -1/2x + 4
1 answer:
Answer:
y=5, x=-2
Step-by-step explanation:
From the graph (attached), we can see that y=5, x=-2.
We can also solve system through algebra. (the easier and faster way)
y=1/2x+6
y=-1/2x+4
Substitute y with the first equation.
1/2x+6=-1/2x+4
1/2x+1/2x=4-6
x=-2
Then, substitute x with -2 in the equation.
y=1/2(-2)+6
y=-1+6
y=5
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Answer:
Option 3: (5, 1)
Step-by-step explanation:
There are several ways of solving for systems of linear equations, either through graphing, substitution, or elimination.
The graphing method is the easiest, as you only need to plot points on the graph using the y-intercepts and the slopes.
I will be demonstrating the <u>graphing method</u>.
Given the systems of linear equations:
Equation 1: y = x - 4
where the <u>slope</u>, <em>m</em> = 1, and <u>y-intercept </u>(0, -4).
Equation2: y = -x + 6
where the <u>slope</u>, <em>m </em>= -1, and <u>y-intercept</u> (0, 6).
The y-intercept is the point on the graph where it crosses the y-axis, and has coordinates of (0, b).
<h3>Graphing Instructions:</h3>For Equation 1, plot the y-intercept, (0, -4) on the graph. Then use the <u>slope</u>, m = 1 (rise 1 unit, run 1 unit) to plot other points on the graph. Repeat this process until you have enough points to connect a line with.
Repeat these same procedures for graphing Equation 2, start by plotting its y-intercept at (0, 6), and its slope, m = -1 (down 1 unit, run 1 unit).
<h3>Solution: </h3>
The intersection of both lines occurs at point, (5, 1), which is solution to the given systems of linear equations. Therefore, the correct answer is the third option, (5, 1).
Attached is the screenshot of the graphed systems of linear equations, where it shows the point of intersection at (5, 1).
