A system of equations is a set of 2 or more equations with the same variables.
A solution to a system of equations is a set of values that makes each equation in the system true.
In this method, you add or subtract the equations to eliminate one of the variables. Follow these steps:
Step 1: Rewrite the equations so that you can add or subtract to eliminate a variable. The coefficients of one of the variables are to be the same number or opposite numbers.
Step 2: Add or subtract the equations to eliminate one of the variables.
Step 3: Solve the equation you get for the variable.
Step 4: Substitute the value you got for the first variable into either of the equations and solve for the second variable.
Solve using elimination.
6x + 4y = –8
–3x − 4y = –16
Step 1: Make sure the equations have opposite x terms or opposite y terms
The y terms (4y and –4y) are already opposites.
Step 2: Add to eliminate the y terms, and then solve for x
6x + 4y = –8
+(-3x – 4y = –16)
3x + 0y = –24
Simplify
3x = – 24
Divide both sides by 3
x = – 8
Step 3: Input the result of Step 2 (x = – 8)into one of the original equations and solve it
6x + 4y = – 8
6( –8) + 4y = – 8
– 48 + 4y = – 8
4y = 40
y = 10
Answer: ( – 8, 10)