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Linear Equations

Solving Systems of Linear Equations by Graphing and Substitution

To solve 2x – 3y = –2 4x + y = 24 you need to solve for y in the second equation by getting the equation to equal y. What would the new equation be? 4x + y = 24 y = –4x + 24 The second equation is equal to y so can begin the next step of putting the value of y into the first equation.
To solve for x you put the second equation into the y value of the first equation and solve. The steps to solve for x would be? 2x – 3(–4x + 24) = –2 2x + 12x – 72 = –2 14x = 70 x = 5
You use the x value to find the y value. If the x=5 what is the equation for the value of y? y = –4(5) + 24 = –20 + 24 = 4 which means y=4
To check your answers to your equation, what would you do? Put the x and y value back into the equation and solve.
This equation has how many solutions? {y=3x+2} {y=-3x+2} This equation only has 1 solution because the graphs will only intersect at one point.Because they have the same slope, they will eventually intersect.
To solve for points on a line equation you must create a T chart with the points of x and y by plugging in a value for x and solving for the value of y. {2x+y=0} {3x+y=1} What would be the coordinates on the graph if x=0? 2(0)+y=0 y=0 The first point on the T chart graphed would be (0,0) because you inserted zero for x and the answer was y=0
If a system simplifies to 0=-2 how many solutions does it have? The system has no solutions because they don't cancel out.
Created by: jackiesheehann