Question

Isolating a variable in two equations is easiest when one of them has a coefficient of 1. let's say we have the two equations 3a−b=5 2a 3b=−4 and want to isolate one of the variables, such that it appears by itself on one side of the equation. which of the following is an equation with one of the above variables isolated?we now have an algebraic expression with only one variable, which can be solved. once we have that, we can plug it back into one of the original equations (or the expression derived in part a) to solve for the other variable. when this is done with the system of two equations from parts a and b, what is the solution? enter a , then b , as two numbers, separated by a comma.

Answer 1

To isolate a variable in two equations, rearrange the equations and solve for one variable by substituting the value back into the original equations.

Step-by-step explanation:

When isolating a variable in two equations, it is easiest when one of the equations has a coefficient of 1. Let's say we have the two equations:

3a - b = 5

2a + 3b = -4

To isolate one of the variables, we can rearrange the equations:

3a - b = 5 ----> b = 3a - 5

2a + 3b = -4 ----> 2a + 3(3a - 5) = -4

Simplifying the second equation:

2a + 9a - 15 = -4 ----> 11a = 11 ----> a = 1

Now we can substitute the value of a back into one of the original equations to solve for b:

3(1) - b = 5 ----> 3 - b = 5 ----> b = -2

Therefore, the solution is a = 1 and b = -2.