Solve by substitution :addition, substration or multiplication
2X+10Y=2 and 3X-5Y=-17
X= Y=
What have you done to try to solve this problem?
To solve the system of equations using substitution, we'll start by solving one equation for one variable and then substitute that expression into the other equation.
Let's solve the first equation for X:
2X + 10Y = 2
To isolate X, we'll subtract 10Y from both sides:
2X = 2 - 10Y
Divide both sides by 2:
X = 1 - 5Y
Now we have an expression for X in terms of Y.
Next, we substitute this value of X into the second equation:
3X - 5Y = -17
Replacing X with 1 - 5Y:
3(1 - 5Y) - 5Y = -17
Distribute 3 to each term inside the parentheses:
3 - 15Y - 5Y = -17
Combine like terms:
-20Y - 12 = -17
Add 12 to both sides:
-20Y = -17 + 12
-20Y = -5
Divide both sides by -20:
Y = (-5) / (-20)
Y = 1/4
Now that we have the value of Y, we can substitute it back into either of the original equations to find X. Let's use the first equation:
2X + 10Y = 2
Substituting Y = 1/4:
2X + 10(1/4) = 2
Simplifying:
2X + 2.5 = 2
Subtract 2.5 from both sides:
2X = 2 - 2.5
2X = -0.5
Divide both sides by 2:
X = (-0.5) / 2
X = -1/4
Therefore, the solution to the system of equations is:
X = -1/4
Y = 1/4