To solve two sets of equations algebraically at the same time:
Here, we are looking to eliminate a variable by substituting one equation into the other.
Example
Number the equations (1) and (2)
Substitute equation (1) into (2)
Solve for x.
Now substitute the value of x back into one of the equations (your choice) and solve for y.
To check your answer, substitute your values for x and y into the equation that you did not use.
Here, we are looking to eliminate a variable by adding both equations.
Example
Notice that adding the equations will lose the y variable.
Number the equations (1) and (2), then add both equations:
Now substitute the value of x back into one of the equations (your choice) and solve for y.
Here, we are looking to eliminate a variable by subtracting one equation from the other.
Example
Notice that subtracting the equations will lose the x variable.
Number the equations (1) and (2), then subtract:
Now substitute the value of y back into one of the equations (your choice) and solve for x.
Here, we are looking to eliminate a variable by first multiplying one equation and then adding or subtracting the equations.
Example
Notice that doubling the bottom equation followed by adding the equations will lose the y variable.
Number the equations (1) and (2), then multiply the bottom equation by 2.
This gives a new equation, which can be added to the top equation:
Now substitute the value of x back into one of the original equations (your choice) and solve for y.
Here, we are looking to eliminate a variable by first multiplying both equations and then adding or subtracting the equations.
Example
Number the equations (1) and (2), then multiply the bottom equation by -3 and the top equation by 2:
This gives two new equations, which can be added to lose the y variable:
Now substitute the value of x back into one of the original equations (your choice) and solve for y.
For solving graphically, click here