True or False: The four regions into which a coordinate plane are divided are called quadrants.
1 answer:
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Answer:
The solution is (0, 2) or x = 0, y = 2.
Step-by-step explanation:
Solving a system of linear equations graphically entails graphing the lines and then finding the point where the lines intersect. This point of intersection will be the solution to the system of equations.
Getting these linear equations into slope-intercept form (y = mx + b, where m is the line's slope and b is the line's y-intercept) makes them a lot easier to graph, so let's make sure that both lines are in slope-intercept form.
The first line isn't in slope-intercept form, so we can rewrite it as:
x + y = 2
y = -x + 2 (Subtract x from both sides of the equation to isolate y)
The second line technically isn't in slope-intercept form, so we can rewrite it as:
y = 2 - 3x
y = -3x + 2 (Commutative Property of Addition)
Now, we can graph the lines to find the solution to the system.
To graph y = -x + 2, draw a line with a slope of -1 (since m = -1) and a y-intercept of (0, 2) (since b = 2). This is the red line on the graph.
To graph y = -3x + 2, draw a line with a slope of -3 (since m = -3) and a y-intercept of (0, 2) (since b = 2). This is the blue line on the graph.
Looking at the graph below, we see that the lines intersect at (0, 2), so this is our answer.
To check if this point is a solution to the system of equations, simply substitute the x and y-coordinates of the point into the equations. If the point satisfies all of the equations, then it is a solution to the system.
In (0, 2), x = 0, and y = 2. Substituting these values into the first equation gives us 0 + 2 = 2, which simplifies to 2 = 2. This is a true statement, so (0, 2) satisfies the first equation. Substituting x = 0 and y = 2 into the second equation gives us 2 = 2 - 3 * 0, which simplifies to 2 = 2. This is also a true statement, so (0, 2) satisfies the second equation, and therefore is a solution to the system of linear equations. Hope this helps!
