Find the solution to the system by the substitution methond.
y=4x-4
y=5x
a.(1,0)
b.(-4,-20)
c.(4,0)
d.(-3,-15)
(Im confused !!!please explain to me how get the answer)!
y = 5 x Divide both sides by 5
y / 5 = x
x = y / 5
y = 4 x - 4
y = 4 * ( y / 5 ) - 4
y = 4 y / 5 - 4 Subtract 4 y / 5 to both sides
y - 4 y / 5 = 4 y / 5 - 4 - 4 y / 5
y - 4 y / 5 = - 4
5 y / 5 - 4 y / 5 = - 4
y / 5 = - 4 Multiply both sides by 5
y = - 20
x = y / 5
x = - 20 / 5
x = - 4
The solutions are:
x = - 4 and y = - 20
Answer b
Since it asked for substitution, why not just sub the 2nd into the 1st
5x = 4x - 4
x = -4
now back into the 2nd:
y = 5x= 5(-4) = -20
so the intersection point is (-4,-20)
To solve the system of equations using the substitution method, we will substitute one equation into the other equation. Let's substitute the value of y from the second equation into the first equation:
Since y = 5x, we can replace y in the first equation with 5x:
4x - 4 = 5x
Now, let's solve this equation for x:
Subtract 4x from both sides to isolate the variable:
-4 = 5x - 4x
Simplifying further:
-4 = x
So, we have found that x = -4.
Now, substitute this value of x back into one of the original equations to solve for y. Let's use the second equation:
y = 5x
y = 5(-4)
y = -20
Therefore, the solution to the system of equations is (-4, -20), which matches option b (-4, -20).