When solving a using , there are three steps.
- Isolate a in one of the .
- Substitute the for that variable into the other equation and solve.
- Substitute this solution into one of the equations and solve for the value of the other variable.
For this exercise, y is already isolated in one equation, so we can skip straight to solving!
y=4x-7 & (I) 3x-2y=-1 & (II)
y=4x-7 3x-2( 4x-7)=-1
y=4x-7 3x-(8x-14)=-1
y=4x-7 3x-8x+14=-1
y=4x-7 -5x+14=-1
y=4x-7 -5x=-15
y=4x-7 5x=15
y=4x-7 x=3
Great! Now, to find the value of y, we need to substitute x=3 into either one of the equations in the given system. Let's use the first equation.
y=4x-7 x=3
y=4( 3)-7 x=3
y=12-7 x=3
y=5 x=3
The solution, or , to this system of equations is the point (3,5). This corresponds to answer choice F.
Checking the Solution
To check our answer, we will substitute our solution into both equations. If doing so results in true statements, then our solution is correct.
y=4x-7 3x-2y=-1
5? =4* 3-7 3* 3-2* 5? =-1
5? =4* 3-7 3* 3-10? =-1
5? =12-7 9-10? =-1
(I): (II): Subtract terms
5=5 -1=-1
Because both equations are true statements, we know that our solution is correct.
