3 Ways to Solve Linear Systems

Solve the system of equations by graphing: -x + 7 = y & x + 1 = y

• (0,6)

• (3,4)

• (-1,5)

• (-2,-2)

You sell small and large candles at a craft fair. You collect $144 by selling 28 total candles. Small candles cost $4 and large candles cost $6. How many of each size of candles did you sell?

• Small: 14 Large: 18

• Small: 7 Large: 11

• Small: 10 Large: 13

• Small: 12 Large: 16

What is the FIRST step to solving systems by elimination?

• Check to see if there is same number opposite sign

• Subtract or add the equations together

• Turn the equations into slope intercept form

• Solve the equations for x

Solve the system of equations by substitution: 5x + 2y = 9 & x + y = -3

• (3,-2)

• (5,-8)

• (4,0)

• (-2,-3)

Solve this system of equations: 4y - 4x = 20 & y = -5

• (-2,-7)

• (1,1)

• (4,-3)

• (0,-5)

Solve the system of equations using elimination: 4x - 3y = 36 & 5x - 2y = -11

• (-2,-4)

• (-7,-12)

• (5,9)

• (0,-10)

What does both equations in a system have to have in order to solve by graphing?

• Same number and variable, opposite signs

• Slope intercept form

• Standard form

• All positive number

Can you substitute if none of the variables are by themselves? (themselves meaning without a constant or being solved for)

• Yes

• No

A farmer plants corn and wheat on a 180-acre farm. The farmer wants to plant three times as many acres of corn as wheat. What is/are the equation(s) used to solve this problem and the amount of acres?

• (y • 3) + x = 180 & x = 6, 120 corn & 40 wheat

• x + y = 180 & 3y = x, 135 corn & 45 wheat

• 3(y + x) = 180, 135 corn & 45 wheat

• x + y = 180 & 3y = x, 90 corn and 30 wheat

What method is the obvious easiest way to solve this system? -x + 4 = y & 2x - 8 = y

• Graphing

• Substitution

• Elimination