Question

What is the solution of the system use substitution
3x-4y=6
5x-2y=-4

Answer 1

To solve the system of equations using substitution, we start by solving one equation for one variable and substituting that expression into the other equation.

Let's solve the first equation for x:

3x - 4y = 6
3x = 6 + 4y
x = (6 + 4y)/3

Now, substitute this expression for x into the second equation:

5x - 2y = -4
5((6 + 4y)/3) - 2y = -4

Multiply both sides by 3 to eliminate the fraction:

5(6 + 4y) - 6y = -12
30 + 20y - 6y = -12
14y + 30 = -12
14y = -42
y = -3

Now substitute this value of y back into the first equation to solve for x:

3x - 4(-3) = 6
3x + 12 = 6
3x = 6 - 12
3x = -6
x = -2

Therefore, the solution to the system of equations is x = -2 and y = -3.