Answer:
x = 3; y = -7
Explanation:
Both equations are solved for y.
Let's substitute what y is equal to in the first equation, -4x + 5, for y in the second equation.
The original second equation is:
y = 3x - 16
Now we plug in -4x + 5 for y in the second equation.
-4x + 5 = 3x - 16
Subtract 3x from both sides.
-7x + 5 = -16
Subtract 5 from both sides.
-7x = -21
Divide both sides by -7.
-7x/-7 = -21/-7
x = 3
Now that we know the value of x, we use substitution again.
Take the first original equation, y = -4x + 5, and substitute 3 for x. Then solve for y.
Here is the first original equation:
y = -4x + 5
Substitute 3 for x:
y = -4(3) + 5
y = -12 + 5
y = -7
The solution is: x = 3; y = -7
We can check the solution to make sure it is correct.
Take each original equation and plug in the values we found for x and y. Simplify both sides and see if they are equal. If the two sides are equal, the solution is correct.
Check first equation:
y = -4x + 5
-7 = -4(3) + 5
-7 = -12 + 5
-7 = -7
The solution works on the first equation.
Check second equation:
y = 3x - 16
-7 = 3(3) - 16
-7 = 9 - 16
-7 = -7
The solution works in the second equation.
This shows that our solution is correct.
Answer: x = 3; y = -7