Answer: The Answer is x=6,y=−1
Step-by-step explanation: (SUBSTITUTION) x=4y+2x+−2=6
Consider the first equation. Subtract 4y from both sides.
x−4y=2x−2
Subtract 2x from both sides.
x−4y−2x=−2
Combine x and −2x to get −x.
−x−4y=−2
Consider the second equation. Add 2 to both sides.
4y+2x=6+2
Add 6 and 2 to get 8.
4y+2x=8
To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.
−x−4y=−2,2x+4y=8
Choose one of the equations and solve it for x by isolating x on the left hand side of the equal sign.
−x−4y=−2
Add 4y to both sides of the equation.
−x=4y−2
Divide both sides by −1.
x=−(4y−2)
Multiply −1 times 4y−2.
x=−4y+2
Substitute −4y+2 for x in the other equation, 2x+4y=8.
2(−4y+2)+4y=8
Multiply 2 times −4y+2.
−8y+4+4y=8
Add −8y to 4y.
−4y+4=8
Subtract 4 from both sides of the equation.
−4y=4
Divide both sides by −4.
y=−1
Substitute −1 for y in x=−4y+2. Because the resulting equation contains only one variable, you can solve for x directly.
x=−4(−1)+2
Multiply −4 times −1.
x=4+2
Add 2 to 4.
x=6
System now finished.
x=6,y=−1
STEPS USING ELIMINATION
x=4y+2x+−2=6
Consider the first equation. Subtract 4y from both sides.
x−4y=2x−2
Subtract 2x from both sides.
x−4y−2x=−2
Combine x and −2x to get −x.
−x−4y=−2
Consider the second equation. Add 2 to both sides.
4y+2x=6+2
Add 6 and 2 to get 8.
4y+2x=8
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.
−x−4y=−2,2x+4y=8
To make −x and 2x equal, multiply all terms on each side of the first equation by 2 and all terms on each side of the second by −1.
2(−1)x+2(−4)y=2(−2),−2x−4y=−8
Simplify.
−2x−8y=−4,−2x−4y=−8
Subtract −2x−4y=−8 from −2x−8y=−4 by subtracting like terms on each side of the equal sign.
−2x+2x−8y+4y=−4+8
Add −2x to 2x. Terms −2x and 2x cancel out, leaving an equation with only one variable that can be solved.
−8y+4y=−4+8
Add −8y to 4y.
−4y=−4+8
Add −4 to 8.
−4y=4
Divide both sides by −4.
y=−1
Substitute −1 for y in 2x+4y=8. Because the resulting equation contains only one variable, you can solve for x directly.
2x+4(−1)=8
Multiply 4 times −1.
2x−4=8
Add 4 to both sides of the equation.
2x=12
Divide both sides by 2.
x=6
The system is now solved.
x=6,y=−1
