Final answer:
To solve the system of equations, one can use the substitution or elimination method. By substituting the expression for y from the second simplified equation into the first, we solve for x and then use this value to find y. The answer will be the intersection point of the two equations.
Step-by-step explanation:
To solve the system of equations given by 10x - y = 5 and 3y = -13x + 92, we first simplify the second equation by dividing by 3, so it becomes y = (-13/3)x + (92/3). Next, we can use substitution or elimination method to find the intersection point. Using substitution, we plug the expression for y from the second equation into the first equation:
10x - ((-13/3)x + (92/3)) = 5Multiply through by 3 to eliminate the fraction: 30x - (-13x) + 92 = 15Combine like terms: 30x + 13x = 15 - 92Solve for x: 43x = -77Divide by 43: x = -77/43Substitute x back into the second equation to find y: y = (-13/3)(-77/43) + (92/3)Simplify to find the value of y.
The solution is the point where both equations intersect, which means the x and y values that satisfy both equations simultaneously.