To solve the system of equations using the substitution method, we’ll first rewrite one of the equations to express one variable in terms of the other.
Let’s take the first equation:
4x + y = 3
We can isolate y:
y = 3 - 4x
Now we have y expressed in terms of x. Next, we will substitute this expression for y into the second equation:
7x + 9y = 2
Substituting the expression we found:
7x + 9(3 - 4x) = 2
Now, expand and simplify this equation:
7x + 27 - 36x = 2
Combine the x terms:
-29x + 27 = 2
Next, isolate x:
-29x = 2 - 27
-29x = -25
x = -25 / -29
x = 25/29
Now that we have the value of x, we can substitute this value back into the equation we found for y:
y = 3 - 4(25/29)
Calculating y:
y = 3 - 100/29
y = (87/29) - (100/29)
y = -13/29
So, the solution to the system of equations is:
(x, y) = (25/29, -13/29)