Solving Systems of Linear Equations by Graphing and Substitution
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| X+Y=7 2x+3y=17 A. Is (4,3) a solution? B. Is (1,6) a solution? | Substitue X and Y with the appropriate numbers. If the left side of the equation equals the right side, the answer is yes. Both answers are yes.
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| Solve by graphing. X+Y=5 -X+Y=-5. | Create a table with a column for X and column for Y and use the value of X (ex: 0,1,2) to solve for Y. Each equation has its own table. Graph two points and notice where the two lines intersect. Answer is (5,0).
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| Solve by substitution. X+Y=8, X=3Y | Since X=3Y, Substitute X in X+Y=8 with 3Y and solve for Y. Next plug in Y into one of the equations and get the answer for X. Solution is (6,2).
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| Solve by substitution. 21X+7Y=22, -3x=Y+6 | Add -6 to both sides to the second equation so Y=-3x-6. Substitute Y in the first equation for Y=-3x-6. Solve for X and Y. You'll notice there is no solution for this equation since the X values cancel out and you're left with two integers.
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| X+Y=9, 2X+3Y=21 A. Is (5,4) a solution? B. Is (6,3) a solution? | Basically substitute the solutions accordingly to their correct positions and determine if they are solutions. A. No B. Yes
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| Solve by graphing. X+Y=3, X+Y=1 | Make tables for each equation using X and Y columns and substitute numbers for X (0,1,2) and solve for Y. Graph two points and notice the lines are parallel to each other and don't intersect. There is no solution.
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| Solve by graphing. Y-2X=-4, -6X+3Y=-12 | Make tables for each and solve for X and Y. Graph two points for each table. Notice the two lines and the same and there are infinite solutions.
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| Solve by substitution. X+10Y=36, 3X+4Y=4 | Get X to equal X=-10Y+36. Substitute X in the second equation with X=-10Y+36 and solve for Y. Plug in the answer for Y in the first equation and solve for X. Answer is (-4,4).
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| Solve without graphing. X=-7, Y=9 A. Do these lines intersect? B.How many solutions does this have? | Since X=-7, this line will be horizontal. Y=9 means the line will be vertical. They will intersect at one point. A.Yes B.Yes
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| Solve without graphing. 9X-Y=12, 1/3Y=-4+3X. A. Do these lines intersect? B. How many solutions does this have? | First, we want to put these equations in slope intercept form. Once that is done, we now look at the y-intercept and slope of both equations. Notice they are both the same meaning they are identical lines with infinite solutions. A.No, parallel B.Infinite
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Or sort by any of the columns using the down arrow next to any column heading.
If you know all the data on any row, you can temporarily remove it by tapping the trash can to the right of the row.
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Created by:
Ali Alaouie
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