To solve the system of equations x/5 + 3y = 22 and 2x - y/7 = 9, we can use the method of substitution. By isolating x in the second equation and substituting it into the first equation, we can solve for y. Then, substituting the value of y back into one of the equations allows us to solve for x. The solutions are x = 134.26 and y = -29.3643.
Step-by-step explanation:
To solve the system of equations, we can use the method of substitution. Step 1: Solve one equation for one variable in terms of the other variable. In the second equation, we can isolate x by multiplying both sides by 7: 2x - y = 63.
Step 2: Substitute the expression for the variable from step 1 into the other equation. Substitute 2x - y for x in the first equation: (2x - y)/5 + 3y = 22.
Step 3: Solve the resulting equation for y. Multiply through by 5 to eliminate the fractions: 2x - y + 15y = 110. Simplify: 15y - y = 110 - 2x. Combine like terms: 14y = 110 - 2x.
Step 4: Solve for y: y = (110 - 2x)/14.
Step 5: Substitute the value of y into one of the equations to solve for x. Substituting the value of y into the first equation: x/5 + 3[(110 - 2x)/14] = 22. Distribute: x/5 + (330 - 6x)/14 = 22.
Multiply through by 70 to eliminate the fractions: 14x + 10[(330 - 6x)/14] = 1540.
Simplify: 14x + 10(330 - 6x)/14 = 1540. Multiply through by 14 to clear the denominator: 14(14x) + 10(330 - 6x) = 14(1540). Simplify: 196x + 3300 - 60x = 21560.
Combine like terms: 136x + 3300 = 21560. Subtract 3300 from both sides: 136x = 18260.
Divide through by 136: x = 134.26. Step 6: Substitute the value of x into one of the original equations to solve for y.
Substituting the value of x into the second equation: 2(134.26) - y/7 = 9. Simplify: 268.52 - y/7 = 9. Multiply through by 7 to eliminate the fraction: 7(268.52) - y = 63.
Divide through by 7: 38.3643- y = 9. Subtract 38.3643 from both sides: - y = 9- 38.3643. Simplify: y = -29.3643. Therefore, x = 134.26 and y = -29.3643.