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Solving Linear Equations by Graphing
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SOLVING SYSTEMS OF LINEAR EQUATIONS BY GRAPHING When given a pair of linear equations, we can graph each linear equation on the same coordinate plane, and then. find the point that both lines have in common. This intersection point is the solution to the system. √x+y=5 L2x-y=4 EXAMPLE: Graph the system of linear equations to find. the solution. 1 The ordered 2 that is the pair solution to both equations. Step 1: Rewrite each of the equations into slope-intercept form (y= mx + b). This will make graphing simpler. Rewrite 1 into slope-intercept form: x+y=5 y = -x + 5 The two lines intersect at (3, 2). Step 2: Graph each of the equations on the same coordinate plane by using the slope and y-intercept of each line. Step 3: Locate the point of intersection. So the solution to the system is (3, 2). Rewrite 2 into slope-intercept form: Check your answer algebraically by substituting the coordinates back into the original system. 2x-y=4 -y = -2x + 4 y=2x-4 A -2 -1 5 4 3 2 1 -1 -2 -3 -4 -5 point of intersection 1 2 3 4 5 x EXAMPLE: Graph the system of linear equations to determine the solution. 2x + y = -2 4x + 2y = 6 Step 1: Rewrite each of the equations in slope-intercept form (y = = mx + b). Rewrite into slope-intercept form: 1 2 2x+y=-2 y=-2x-2 Step 3: Locate the point of intersection. Step 2: Graph each of the equations on the same coordinate plane by using the slope and y-intercept of each line. There are NO intersection points. So there is NO SOLUTION to the...
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Alternative transcript:
system. same slope, different y-intercepts Rewrite 2 into slope-intercept form: 4x+2y=6 2y=-4x+6 y=-2x+3 -5 -4 -3 -2 Y -1 5 4 3 2 1 -2 -3 -4 -S 1 2 3 4 5 א CAP 1 + EXAMPLE: Graph the system of linear equations to find the solution. 1 4x - 2y = 6 2x - y = 3 2 Step 1: Rewrite each equation in slope-intercept form. 1 4x - 2y = 6 -2y = -4x+6 y=2x-3 Step 2: Graph the equations on the same coordinate plane. Step 3: Locate the point of intersection. + 22x-y-3 There are an infinite number of solutions because there are an infinite number of points. where the lines overlap. The graphs represent the same line, so the equations are EQUIVALENT. SAME SLOPE and the SAME y-intercepts = + INFINITE solutions -y=-2x+3 y=2x-3 -3 -2 Y -1 5 4 3 2 1 -1- -2 -3 A -5 1 2 3 4 5 x
Solving Linear Equations by Graphing
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Clara Vandenbelt
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Learn how to find the solution to a system of linear equations by graphing them on the same coordinate plane.
Clara Vandenbelt
105 Followers
Learn how to find the solution to a system of linear equations by graphing them on the same coordinate plane.
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SOLVING SYSTEMS OF LINEAR EQUATIONS BY GRAPHING When given a pair of linear equations, we can graph each linear equation on the same coordinate plane, and then. find the point that both lines have in common. This intersection point is the solution to the system. √x+y=5 L2x-y=4 EXAMPLE: Graph the system of linear equations to find. the solution. 1 The ordered 2 that is the pair solution to both equations. Step 1: Rewrite each of the equations into slope-intercept form (y= mx + b). This will make graphing simpler. Rewrite 1 into slope-intercept form: x+y=5 y = -x + 5 The two lines intersect at (3, 2). Step 2: Graph each of the equations on the same coordinate plane by using the slope and y-intercept of each line. Step 3: Locate the point of intersection. So the solution to the system is (3, 2). Rewrite 2 into slope-intercept form: Check your answer algebraically by substituting the coordinates back into the original system. 2x-y=4 -y = -2x + 4 y=2x-4 A -2 -1 5 4 3 2 1 -1 -2 -3 -4 -5 point of intersection 1 2 3 4 5 x EXAMPLE: Graph the system of linear equations to determine the solution. 2x + y = -2 4x + 2y = 6 Step 1: Rewrite each of the equations in slope-intercept form (y = = mx + b). Rewrite into slope-intercept form: 1 2 2x+y=-2 y=-2x-2 Step 3: Locate the point of intersection. Step 2: Graph each of the equations on the same coordinate plane by using the slope and y-intercept of each line. There are NO intersection points. So there is NO SOLUTION to the...
SOLVING SYSTEMS OF LINEAR EQUATIONS BY GRAPHING When given a pair of linear equations, we can graph each linear equation on the same coordinate plane, and then. find the point that both lines have in common. This intersection point is the solution to the system. √x+y=5 L2x-y=4 EXAMPLE: Graph the system of linear equations to find. the solution. 1 The ordered 2 that is the pair solution to both equations. Step 1: Rewrite each of the equations into slope-intercept form (y= mx + b). This will make graphing simpler. Rewrite 1 into slope-intercept form: x+y=5 y = -x + 5 The two lines intersect at (3, 2). Step 2: Graph each of the equations on the same coordinate plane by using the slope and y-intercept of each line. Step 3: Locate the point of intersection. So the solution to the system is (3, 2). Rewrite 2 into slope-intercept form: Check your answer algebraically by substituting the coordinates back into the original system. 2x-y=4 -y = -2x + 4 y=2x-4 A -2 -1 5 4 3 2 1 -1 -2 -3 -4 -5 point of intersection 1 2 3 4 5 x EXAMPLE: Graph the system of linear equations to determine the solution. 2x + y = -2 4x + 2y = 6 Step 1: Rewrite each of the equations in slope-intercept form (y = = mx + b). Rewrite into slope-intercept form: 1 2 2x+y=-2 y=-2x-2 Step 3: Locate the point of intersection. Step 2: Graph each of the equations on the same coordinate plane by using the slope and y-intercept of each line. There are NO intersection points. So there is NO SOLUTION to the...
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Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.
Still not sure? Look at what your fellow peers are saying...
iOS User
I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D
Stefan S, iOS User
The application is very simple and well designed. So far I have found what I was looking for :D
SuSSan, iOS User
Love this App ❤️, I use it basically all the time whenever I'm studying
Alternative transcript:
system. same slope, different y-intercepts Rewrite 2 into slope-intercept form: 4x+2y=6 2y=-4x+6 y=-2x+3 -5 -4 -3 -2 Y -1 5 4 3 2 1 -2 -3 -4 -S 1 2 3 4 5 א CAP 1 + EXAMPLE: Graph the system of linear equations to find the solution. 1 4x - 2y = 6 2x - y = 3 2 Step 1: Rewrite each equation in slope-intercept form. 1 4x - 2y = 6 -2y = -4x+6 y=2x-3 Step 2: Graph the equations on the same coordinate plane. Step 3: Locate the point of intersection. + 22x-y-3 There are an infinite number of solutions because there are an infinite number of points. where the lines overlap. The graphs represent the same line, so the equations are EQUIVALENT. SAME SLOPE and the SAME y-intercepts = + INFINITE solutions -y=-2x+3 y=2x-3 -3 -2 Y -1 5 4 3 2 1 -1- -2 -3 A -5 1 2 3 4 5 x