Elimination+Level+3

Grade 10 Math Systems of Equations Elimination Elimination Level 1 Elimination Level 2

1) 2x + 3y = 23 2) 3x - y = 7
 * Level 3: Multiplication of one equation**

Notice how the y-terms are opposite signs but different values? If you multiply one of the equations to make the value of the y-terms the same, then the y-term will be eliminated when you add the equations.

1) 2x + 3y = 23 3 x 2) 9x - 3y = 21 [Multiply the 2nd equation by 3]

11x = 44 [Solve] x = 4

Substitute x = 4 in 1) [Substitute the found value into one of the equations to solve for the other variable] 1) 2x + 3y = 23 2(4) + 3y = 23 [Solve] 8 + 3y = 23 3y = 23 - 8 3y = 15 y = 5

Check (4, 5) in 2) [Check the solution in the other equation]

2) 3x - y = 7 L.S. = 3x - 4y R.S. = 7 = 3(4) - (5) = 12 - 5 = 7 = R.S.

Therefore, the solution to the system is (4, 5) [State the solution]