Answer:
[tex]\boxed {\boxed {\sf (1, 3) \ or \ x=1 \ and \ y=3}}}[/tex]
Step-by-step explanation:
We are given this system of equations:
[tex]4x+y=7\\4x-2y=-2[/tex]
We use elimination to solve to eliminate one of the variables, so we only have to work with one at a time. We do this by adding and subtracting the equations, and sometimes multiplying the entire equation by a number.
Notice how both equations have a 4x. This means they can easily be eliminated, without multiplying the equations by another number first. Let's subtract the 2 equations.
[tex]\ \ \ 4x+y=7\\ -(4x-2y)=-2[/tex]
The 4x will cancel because 4x-4x=0.
[tex]\ \ \ \ y=7 \\ - (-2y) = -2[/tex]
Since there are back to back negative signs, they become addition signs.
[tex]\ \ \ \ y=7 \\+2y=2[/tex]
[tex]3y=9[/tex]
We are solving for y , so we must isolate the variable. It is being multiplied by 3 and the inverse of multiplication is division. Divide both sides by 3.
[tex]3y/3=9/3\\y=3[/tex]
Now we can substitute 3 in for y in the original equations. Let's use the first one.
[tex]4x+y=7\\4x+3=7[/tex]
3 is being added to 4x. The inverse of addition is subtraction. Subtract 3 from both sides.
[tex]4x+3-3=7-3\\4x=4\\[/tex]
x is being multiplied by 4. The inverse of multiplication is division. Divide both sides by 4.
[tex]4x/4=4/4\\x=1[/tex]
x is equal to 1 and y is equal to 3. Coordinate points are written as (x, y). The solution to this system of equations is (1, 3).
