Systems of Equations Exercises

Solve this system of linear equations using the elimination method:

3x – 3y = -9
4x + 8y = -24

Hint

Multiply Row 1 by -4 and Row 2 by 3. Then add the equations together which will eliminate the x's.

Find the solution to this system of equations using the substitution method:

Hint

Substitute the into the y value of the first equation.

Find the solution to the non-linear system of equations algebraically.

y = x² + 1
y = – 2x

Hint

Substitute the x² + 1 into the y value of the second equation. This one can be factored!

Find the solution to this system of equations using a graphing calculator:

y = e^{x + 1}
y = -2x² – 8

Hint

Type each equation into your favorite graphing calculator or website grapher and find where they intersect.

Solve this system of equations by any method.

2x + 5y = 3
4x + 10y = 6

Hint

How about the elimination method? Try multiplying Row 1 by -2.