Final answer:
To solve the system of equations by substitution, use the second equation to express y in terms of x, substitute into the first equation, and solve for x. Then, substitute the value of x back into the second equation to find y. The solution is x = -6 and y = -36.
Step-by-step explanation:
To solve the given system of equations by substitution, we can start by using the second equation 6x = y to substitute for y in the first equation.
- First, we rewrite the equation 6x = y as y = 6x.
- Now we substitute y in the first equation: -5x + 2(6x) = -42 becomes -5x + 12x = -42.
- This simplifies to 7x = -42. Divide both sides by 7 to find x = -6.
- Substitute x = -6 back into y = 6x to find y: y = 6(-6) which simplifies to y = -36.
The solution to the system of equations is x = -6 and y = -36. This is the point where the two lines would intersect on a graph.