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## What is a System of Equations?

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**What is a System of Equations?**• Use the iPads to find information about: • Uses • Ways to solve • Real-world applications • Types • Vocabulary**Can you look at a system of linear equations and tell how**many solutions it has? For example: Could you tell that the equations y=2x +1 and y= 2x-7 have no solution?**In this lesson you will learn to predict how many solutions**a system of linear equations has by inspection.**Slope Intercept Form of an Equation**y = mx + b slope y-intercept**Graphing a linear equation**y = 2x + 1 slope y-intercept**Assuming that all equations have one solution because those**are the types of equations that are solved the most.**There are three types of solutions for systems of linear**equations One None Infinitely Many**y = x - 5**y = 4x +4 y = 2x + 1 y = x - 3 y = 4(x+1) y = 3x + 1 Same Line infinitely many solutions Parallel lines no solution One point one solution**Determine the number of solutions that the system has.**Slope: -4, y-intercept: -16 y = -4(x+4) y = -4x-16 Slope: -4, y-intercept: -16 y = -4x-16**Determine the number of solutions that the system has.**Slope: 1, y-intercept: 1 y = x + 1 Slope: , y-intercept: 1 y = x + 1**Determine the number of solutions that the system has.**Slope: -5, y-intercept: 1 y = -5x + 1 Slope: -5, y-intercept: -2 y = -5x-2**How many solutions does the system of linear equations have?**y= -2x+1 y= -2x-2**How many solutions does the system of linear equations have?**y= -3x+1 y= -2x-7**How many solutions does the system of linear equations have?**y= -3(x+1) y= -3x-3**Create a second equation for the following system of**equations so that they have one solution, no solution, and infinitely many solutions. • One solution • y = 7x + 1 y= • No solution • y = 7x + 1 y= • Infinitely many solutions • y = 7x + 1 y=**How many solutions does the system of equations have?**y=6(x+1) and y=6x+6 a) One b) None c) Infinitely Many How many solutions does the system of equations have? y=-3x and y=x+1 a) One b) None c) Infinitely Many**What happens if we graph a system of equations and the lines**intersect? y = x-1 y = 2x-2**Not having the equation in slope- intercept form**y = 2 -x 3x + 2y = 4 y = -x + 2 -3x = -3x 2y = 4 -3x Slope: -, y-intercept: 2 2 = 2**Graph the system of linear equations. Determine their**solution. y = x-1 y -2x = 2 +2x = +2x y = 2 + 2x y = 2x + 2**Graph the system of linear equations. Determine their**solution. Slope: 1, y-intercept: -1 y = x-1 Slope: 2, y-intercept: -2 y = 2x-2**y = x-1**0 = 1-1 0 = 0 (1,0) y = 2x-2 0 = 2*1-2 0 = 0**Graph the system of linear equations. Determine their**solution. y = x+3 -4x + y = 0 +4x = +4x y = 4x**Graph the system of linear equations. Determine their**solution. Slope: 4, y-intercept: 0 y = 4x Slope: 1, y-intercept: 3 y = x+3**y = 4x**4 = 4*1 (1,4) 4 = 4 y = x+3 4 = 1+3 4 = 4**When we solve the systems of equations y=2x and y=x, what is**our solution? What does it mean?**How many solutions does the system of equations y=2x+1 and**y=x+1 have? Why?**The solution for the system of linear equations y=3x+4 and**y=x+2 is? a) (-1,1) b) (1,-1) c)(-1,-1) d) (1,1) The solution for the system of linear equations y=x+6 and y=-2x is? a) (2,-4) b) (-2,4) c) (-2,-4) d) (2,4)**What happens if we graph a system of equations and the lines**are parallel? y = x y = x- 1**Graph the system of linear equations. Determine their**solution. y - 4 = 2x y = 2x + 4 = + 4 y = 2x + 4**Graph the system of linear equations. Determine their**solution. Slope: 2, y-intercept: 0 y = 2x Slope: 2, y-intercept: 4 y = 2x+4**y = 2x**y = 2x+4**Graph the system of linear equations. Determine their**solution. -x + 2y = 0 2y –x = - 2 +x = +x +x = +x 2y = x - 2 2y = x 2 = 2 2 = 2 y = x- 1 y = x**Graph the system of linear equations. Determine their**solution. Slope: , y-intercept: 0 y = x Slope: , y-intercept: -1 y = x- 1**y = x**y = x- 1**y = x**y = x- 1**Find the solution for the system of linear equations y=3x**and y=3x-2 by graphing.**The solution for the system of linear equations y=2x+1 and**y=2x-3 is? a) (-1,1) b) (1,-1) c)(-1,-1) d) no solution The solution for the system of linear equations y=-x+6 and y=-x-2 is? a) (2,-4) b) (-2,4) c) (-2,-4) d) no solution**What happens if we graph a system of equations and the lines**are the same? y = 2(2x+4) y = 4x+8**Graph the system of linear equations. Determine their**solution. y = 2(2x+4) y – 4x = 8 y = 4x+8 +4x = +4x y = 4x + 8**Graph the system of linear equations. Determine their**solution. Slope: 4, y-intercept: 8 y = 2(2x+4) y = 4x+8 Slope: 4, y-intercept: 8 y = 4x+8**y = 2(2x+4)**y = 4x+8 y = 4x+8**Graph the system of linear equations. Determine their**solution. x -y = -1 y =x-2+3 -x =-x y =x+1 -y = -1-x -1 = -1 y= 1 +x y= x + 1**Graph the system of linear equations. Determine their**solution. Slope:1, y-intercept: 1 y =x+1 Slope:1, y-intercept: 1 y =x-2+3 y =x+1**y =x+1**y =x-2+3 y =x+1**y-3x = 3**y =3(x+1)**The solution for the system of linear equations y=2x+1 and**y=2x-3 is? a) One solution b)Infinitely Many Solutions The solution for the system of linear equations y=4x-12and y=4(x+3)is? a) One solution b) Infinitely Many Solutions