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.
Answer
(-4, -1)
Example 2
Find the solution to this system of equations using the substitution method:
Hint
Substitute the into the y value of the first equation.
Answer
What happened? -18 cannot equal 3. There is no solution because the lines are parallel and will never intersect.
Example 3
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!
Answer
(-1, 2)
Example 4
Find the solution to this system of equations using a graphing calculator:
y = ex + 1 y = -2x2 – 8
Hint
Type each equation into your favorite graphing calculator or website grapher and find where they intersect.
Answer
No solution! The two functions don't ever intersect.
Example 5
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.
Answer
This might not make any sense, but all the variables cancelled out. And the left and right side of what you are left with is equal. This means there are infinitely many solutions because the two lines are the same line.
into the y value of the first equation.