To solve this system of equations, we can use either substitution or elimination method.
Method 1: Substitution
Step 1: Solve one equation for one variable in terms of the other variable.
Let's solve the first equation for x:
2x + 4y = 10
2x = 10 - 4y
x = 5 - 2y
Step 2: Substitute this expression for x in the second equation.
3x + 5y = 11
3(5 - 2y) + 5y = 11
15 - 6y + 5y = 11
-y = 11 - 15
-y = -4
y = 4
Step 3: Substitute the value of y back into x = 5 - 2y to find x.
x = 5 - 2(4)
x = 5 - 8
x = -3
The solution to the system of equations is x = -3 and y = 4.
Method 2: Elimination
Step 1: Multiply the first equation by 3 and the second equation by 2 to make the coefficients of x the same.
3(2x + 4y) = 3(10)
2(3x + 5y) = 2(11)
6x + 12y = 30
6x + 10y = 22
Step 2: Subtract the second equation from the first equation to eliminate x.
(6x + 12y) - (6x + 10y) = 30 - 22
2y = 8
y = 4
Step 3: Substitute the value of y back into the first equation to find x.
2x + 4(4) = 10
2x + 16 = 10
2x = 10 - 16
2x = -6
x = -3
The solution to the system of equations is x = -3 and y = 4.
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Use substitution or elimination to find the solution to the system of equations. Show all work.
2x+4y=10
3x+5y=11
1 answer
52 answers