Final answer:
To solve the system of linear equations, we can use elimination by multiplication. Multiply the second equation by 2 to make the coefficient of y the same in both equations. Then, subtract the equations to eliminate the x variable and solve for y. Finally, substitute the value of y back into one of the original equations to solve for x.
Step-by-step explanation:
To solve the system of linear equations using elimination by multiplication, we need to multiply one or both of the equations so that one of the variables has the same coefficient with the opposite sign. Let's choose the second equation and multiply both sides by 2 to make the coefficient of y in both equations the same.
2(2x + 4y) = 2(7)
4x + 8y = 14
Now, we can subtract the equations to eliminate the x variable.
(4x + 5y) - (4x + 8y) = 5 - 14
-3y = -9
To isolate y, divide both sides by -3.
y = 3
Now that we know the value of y, we can substitute it back into one of the original equations to find x.
4x + 5(3) = 5
4x + 15 = 5
Subtract 15 from both sides.
4x = -10
To isolate x, divide both sides by 4.
x = -2.5
Therefore, the solution to the system of linear equations is x = -2.5 and y = 3.