Explanation:
Let's solve the first system of equations using substitution. The example is:
1)
3x - 4y = 2
-2x + 6y = -18
Step 1: Solve one equation for one variable.
Let’s solve the first equation for x.
3x - 4y = 2
Add 4y to both sides:
3x = 2 + 4y
Divide both sides by 3:
x = (2 + 4y)/3
Step 2: Substitute this expression for x into the second equation.
Second equation:
-2x + 6y = -18
Substitute x:
-2*( (2 + 4y)/3 ) + 6y = -18
Multiply:
(-4 - 8y)/3 + 6y = -18
To eliminate fractions, multiply every term by 3:
-4 - 8y + 18y = -54
Combine like terms:
-4 + 10y = -54
Add 4 to both sides:
10y = -50
Divide by 10:
y = -5
Step 3: Plug y = -5 back into the expression for x.
x = (2 + 4*(-5))/3
x = (2 - 20)/3
x = (-18)/3
x = -6
So, x = -6, y = -5
Step 4: Check the solution in both original equations.
First equation:
3x - 4y = 2
3*(-6) - 4*(-5) = -18 + 20 = 2
✔
Second equation:
-2x + 6y = -18
-2*(-6) + 6*(-5) = 12 - 30 = -18
✔
Both equations are true, so the solution is correct.
Final Answer:
x = -6, y = -5
Parent Tip: Review the logic above to help your child master the concept of elimination systems of equations worksheet.
