To find the solution to the system of linear equations:
4x + 6y = 20
-5x + 7y = 62
We can use the method of substitution or elimination to solve for x and y. Let's use the elimination method:
1. Multiply the first equation by 5 and the second equation by 4 to eliminate the x variable:
20x + 30y = 100
-20x + 28y = 248
2. Add the two equations together:
(20x - 20x) + (30y + 28y) = 100 + 248
58y = 348
3. Divide both sides of the equation by 58:
y = 6
4. Substitute the value of y back into either of the original equations. Let's use the first equation:
4x + 6(6) = 20
4x + 36 = 20
4x = 20 - 36
4x = -16
x = -4
Therefore, the solution to the system of linear equations is:
(x, y) = (-4, 6)