Question

Given the equations:

1.8 = 5.4x - y
y = -3.8 - 6.2x

What is the solution for x?

a) x = 0.2
b) x = -0.2
c) x = 0.3
d) x = -0.3

Answer 1

To solve the system of equations, the second equation is substituted into the first one, resulting in the value of x being approximately -0.2. The solution of x is 0.1724

Step-by-step explanation:

This is asked to solve a system of linear equations to find the value of x. We have two equations: 1.8 = 5.4x - y, y = -3.8 - 6.2x. To find the solution for x, we can substitute the second equation into the first one: 1.8 = 5.4x - (-3.8 - 6.2x), 1.8 = 5.4x + 3.8 + 6.2x, 1.8 = 11.6x + 3.8, 1.8 - 3.8 = 11.6x, -2.0 = 11.6x, x = -2.0 / 11.6, x = -0.1724...Looking at the given options, the closest value to the calculated x is -0.2 (Option b). Substituting the expression for y into the first equation and simplifying, the solution for x is approximately -0.1724. The closest match among the options is -0.2 (Option b). This demonstrates the process of substitution in solving a system of linear equations to find the value of x.