Answer:
x = 1, y = −1
Step-by-step explanation:
21x + 7y = 14, −7y = 10 − 3x
Consider the second equation. Add 3x to both sides.
−7y + 3x = 10
In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.
21x + 7y = 14, 3x − 7y = 10
To make 21x and 3x equal, multiply all terms on each side of the first equation by 3 and all terms on each side of the second by 21.
3 × 21x + 3 × 7y = 3 × 14, 21 × 3x + 21 (−7)y = 21 × 10
Simplify.
63x + 21y = 42, 63x − 147y = 210
Subtract 63x − 147y = 210 from 63x + 21y = 42 by subtracting like terms on each side of the equal sign.
63x − 63x + 21y + 147y = 42 − 210
Subtract 63x from 63x. Terms 63x and −63x cancel out, leaving an equation with only one variable that can be solved.
21y + 147y = 42 − 210
Add 21y to 147y.
168y = 42 − 210
Subtract 210 from 42.
168y = −168
Divide both sides by 168.
y = −1
Substitute −1 for y in 3x − 7y = 10. Because the resulting equation contains only one variable, you can solve for x directly.
3x − 7 (−1) = 10
Multiply −7 times −1.
3x + 7 = 10
Subtract 7 from both sides of the equation.
3x = 3
Divide both sides by 3.
x = 1
Now we have our answer
x = 1, y = −1
