Solve the System of Linear Equations
Introduction to Solving Systems of Linear Equations
Linear equations are algebraic expressions that represent straight lines on a graph. When we have a system of linear equations, we are dealing with multiple linear equations simultaneously. To solve a system of linear equations, we can use different methods such as substitution, elimination, or graphing.
Using Elimination to Solve the System of Linear Equations
In the given system of equations:
-3x - 5y = -15
-3x - 3y = -3
We can use the elimination method to solve the system. By adding the two equations together, we can eliminate the variable x:
-3x - 5y = -15
-3x - 3y = -3
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-8y = -18
y = 6
Substitute the value of y back into one of the equations to solve for x:
-3x - 5(6) = -15
-3x - 30 = -15
-3x = 15
x = -5
Therefore, the solution to the system of linear equations is (-5,6). This means that the point of intersection for the two lines represented by the equations is at x = -5 and y = 6.