Question

Use the addition method.
5x−7y=4
7x−5y=5

Answer 1

To solve the given system of equations using the addition method, multiply the equations by appropriate numbers to make the coefficients opposite, and then subtract one equation from the other to eliminate a variable. Solve for the remaining variable and substitute its value back into one of the original equations to find the other variable.

Step-by-step explanation:

To solve the system of equations using the addition method, follow these steps:

1. Multiply the equations by appropriate numbers so that the coefficients of either x or y will be opposite. In this case, we multiply the first equation by 7 and the second equation by 5, resulting in:

• 35x - 49y = 28
• 35x - 25y = 25

Subtract the second equation from the first equation to eliminate the x-term. This gives:

• -24y = 3

Divide both sides of the equation by -24:

• y = -3/24

Substitute the value of y into either of the original equations and solve for x:

• 5x - 7(-3/24) = 4
• 5x + 21/24 = 4
• 5x = 4 - 21/24
• 5x = 96/24 - 21/24
• 5x = 75/24
• x = 75/24 ÷ 5/1
• x = 75/24 * 1/5
• x = 75/120
• x = 5/8

Therefore, the solution to the system of equations is x = 5/8 and y = -3/24.