How do you solve y=2x-5 and 4x-y=7 using substitution?
1 Answer
Explanation:
In order to solve a system of equations using substitution, you must express one variable in terms of the other in one equation, then use this value in the second equation.
Your system of two equations with two unknowns,
{(y = 2x - 5), (4x-y = 7):}
Notice that the first equation has
y = color(blue)(2x - 5)
Use this value of
4x - overbrace((color(blue)(2x-5)))^(color(purple)("= y")) = 7
4x - 2x + 5 = 7
2x = 2 implies x = 2/2 = 1
Now take this value of
y = 2 * 1 - 5 = -3
The solution to your system of equations is
{(x=1), (y=-3) :}
Notice that you can find the same values for
4x = 7 + y implies x = color(blue)((7+y)/4)
Substitute this into the first equation to find the value of
y = 2 * overbrace((color(blue)((7+y)/4)))^(color(purple)("= x")) - 5
y = (7 + y)/2 - 5
Multiply all the terms by
2y = 7 + y - 10
Rearrange to find
y = -3
This will once again get you
x = (7 + (-3))/4 = 4/4 = 1