0 and 2
f(x) = g(x) will be the input or x value at which f and g have the same output or y value. Look in the table where two numbers repeat right next to each other.
−1 −7/2 −9/2
0 −3 −3
1 −2 −3/2
2 0 0
3 4 3/2
4 12 3
5 28 9/2
There are two solutions to f(x) = g(x) which are x=0 and x=2.
That would be 3.5 b/c it can’t be expressed as a ratio or a simple fraction
To solve the system of equations, we first need to isolate one of the variables in one of the equations. For this example, I'll isolate x from the second equation, because it will be much easier and I'll end up with simpler fractions.
2x + y = -3 Given
2x = -y - 3 Subtract y from both sides
x = -1/2y - 3/2
Now, we need to substitute x in the other equation for -1/2y - 3/2 so that we can find y.
3(-1/2y - 3/2) - 7y = 4 Substitute
-3/2y - 9/2 - 7y = 4 Multiply
-17/2y - 9/2 = 4 Collect like terms (wow, this is turning out to be a tough one, isn't it?)
-17/2y = 17/2
y = -1
Wow, such complicated work for such a simple answer. Anyway, now we can plug that into our answer for x to get x's value.
<span>x = -1/2y - 3/2 Given
</span>x = -1/2(-1) - 3/2 Substitute
x = 1/2 - 3/2 Multiply
x = -1 Subtract
Therefore, the solution for the system of equations is (-1,-1). It can be a bit intimidating with all the fractions, but the question decided to be nice and give us simple answers.
Hope this helps!
