y=-2x+2, 7x+4y=7
2x+y=2 or 8x+4y=8
7x+4y=7. Subtracting one eq from other, we get x=1. Substituting this in given eq, 2x1+y=2 or y=0.
Check:0=-2x1+2 ok,
7x1+4x0=7 ok.
ideal setup for "substitution"
1st into 2nd:
7x + 4(-2x+2) = 7
7x + 8x + 8= 7
-x = -1
x = 1
plug that back into 1st, all done
To solve these equations, we can use either substitution or elimination method. Let's solve them using the elimination method:
Step 1: Multiply the first equation by 2 to make the coefficient of 'y' in both equations the same:
2y = -4x + 4
Step 2: Rewrite the second equation:
7x + 4y = 7
Step 3: Multiply the second equation by -1 to make the coefficient of 'y' the same:
-7x - 4y = -7
Step 4: Add the two equations together:
(2y) + (-4y) = (-4x + 4) + (-7x - 4)
-2y = -4x - 7x + 4 - 4
-2y = -11x
Step 5: Divide both sides of the equation by -2 to isolate 'y':
y = (-11x) / -2
y = (11x) / 2
So the solution to the system of equations is y = (11x) / 2.
You can also represent the solution in the form of an equation by substituting the value of 'y' derived from one equation into the other equation:
7x + 4((11x)/2) = 7
Simplify the equation:
7x + 22x = 7
29x = 7
Divide both sides by 29:
x = 7/29
Therefore, the solution to the system of equations is x = 7/29 and y = (11x)/2.