Final answer:
To solve the system of equations (5r + 3y = 2, y = 2r - 3), use the substitution method, where y is already isolated in the second equation. Substitute y into the first equation and solve for r, then use r to find y. The solution is r = 1 and y = -1.
Step-by-step explanation:
The student is asking to solve a system of equations, which involves finding the values of the variables that make both equations true at the same time. The system given is:
1. 5r + 3y = 2
2. y = 2r - 3
To find the solution, we can use the substitution method. Here's a step-by-step explanation:
1. Identify the equations given. We have two equations: 5r + 3y = 2 and y = 2r - 3.
2. Isolate one variable in one equation. The second equation is already solved for y, so we can use this to substitute for y in the first equation.
3. Substitute the expression for y from the second equation into the first equation: 5r + 3(2r - 3) = 2.
4. Simplify and solve for r. This gives us 5r + 6r - 9 = 2, which simplifies to 11r - 9 = 2 and then 11r = 11. Dividing by 11, we find r = 1.
5. Substitute r back into the second equation to find y: y = 2(1) - 3, which simplifies to y = -1.
6. We now have the solution: r = 1 and y = -1.
The solution to the system of equations is r = 1 and y = -1.