To solve the system of linear equations given by:
1. 2x + y = 5
2. 3x + 2y = 4
we can use the substitution or elimination method. Here, we’ll use the substitution method.
First, let’s solve the first equation for y:
y = 5 – 2x
Now that we have y in terms of x, we can substitute this expression for y into the second equation:
3x + 2(5 – 2x) = 4
Expanding this gives us:
3x + 10 – 4x = 4
Simplifying it leads to:
-x + 10 = 4
Next, we can isolate x:
-x = 4 – 10
-x = -6
x = 6
Now that we have x, we can substitute it back into the equation for y
y = 5 – 2(6)
This simplifies to:
y = 5 – 12
y = -7
Thus, the solution to the system of equations is:
(x, y) = (6, -7)