Answer:
To solve a system of equations by substitution, we can use one equation to solve for one variable in terms of the other variable, and then substitute that expression into the other equation.
Given the system of equations:
10x + 2y = 4
.-9x + 3y = 18
We can start by isolating y in one of the equations. For example, we can use the first equation:
10x + 2y = 4
To solve for y, we can divide both sides by 2:
y = -5x + 2
Now we can substitute this expression for y into the second equation:
-9x + 3(-5x + 2) = 18
-9x - 15x + 6 = 18
-24x + 6 = 18
-24x = 12
x = -0.5
Now that we know x = -0.5, we can substitute this value back into the original expression we found for y:
y = -5(-0.5) + 2
y = 2.5
So the solution of the system of equations is (x, y) = (-0.5, 2.5).