Question

use the substitution method to solve the system of equations
2y+4x=18
2y-3x=4

Answer 1

To solve the system of equations using the substitution method, we first solve one equation for one variable and substitute it into the other equation.

Let's solve the first equation for y:
2y + 4x = 18
2y = 18 - 4x
y = (18 - 4x)/2
y = 9 - 2x

Now substitute this expression for y in the second equation:
2y - 3x = 4
2(9 - 2x) - 3x = 4
18 - 4x - 3x = 4
-7x + 18 = 4
-7x = 4 - 18
-7x = -14
x = -14 / -7
x = 2

Now substitute x = 2 back into the first equation to find y:
2y + 4x = 18
2y + 4(2) = 18
2y + 8 = 18
2y = 18 - 8
2y = 10
y = 10 / 2
y = 5

Therefore, the solution to the system of equations is x = 2 and y = 5.