Solve a System of Equations Using Elimination
Some systems of equations are more easily solved using the elimination method. The elimination method involves multiplying and combining equations in a system in order to eliminate a variable.
Solve the following system of equations using the elimination method:
4x + 3y = -2
5x – y = 7
The first step is to pick one variable to eliminate. For a variable to eliminate when the equations are added together, the coefficients must have opposite values. In this case we will be eliminating the y variable. In order to do this, we need to multiply the second equation by 3.
3[5x – y = 7]
15x – 3y = 21
Notice that the coefficient of y in the first equation is positive 3 and the coefficient on y in the second equation is negative 3. Now we can combine our equations:
4x + 3y = -2
+ 15x – 3y = 21 (Addition Property of Equality)
19x + 0y = 19
The y term has been 'eliminated'.
19x = 19
x = 1
The final step is to solve for y using x = 1.
The final answer is (1, -2).4x + 3y = -2
4(1) + 3y = -2
4 + 3y = -2
3y = -6
y = -2
