How to solve the system of equations:
\[ 4x + 5y = 11 \]
\[ 2x + 6y = 16 \]
Show the steps, please.
Answer (3)
4x+5y = 11 and 2x+6y = 16 Let's start by solving 4x+5y = 11 for the variable x. Move the 5y to the right hand side by subtracting 5y from both sides, like this: From the left hand side: 5y - 5y = 0 The answer is 4x From the right hand side: The answer is 11-5y Now, the equation reads: 4x = 11-5y To isolate the x, we have to divide both sides of the equation by theother variables around the x on the left side of the equation. The last step is to divide both sides of the equation by 4 like this: To divide x by 1 The x just gets copied along in the numerator. The answer is x 4x ÷ 4 = x To divide 11-5y by 4 divide each term in 11-5y by 4 term by term. 11 ÷ 4 = 11/4 ** To divide y by 1 The y just gets copied along in the numerator. -5y ÷ 4 = The solution to your equation is: x = Next, let's solve 2x+6y = 16 for the variable y. Move the 2x to the right hand side by subtracting 2x from both sides, like this: From the left hand side: 2x - 2x = 0 The answer is 6y From the right hand side: The answer is 16-2x Now, the equation reads: 6y = 16-2x To isolate the y, we have to divide both sides of the equation by theother variables around the y on the left side of the equation. The last step is to divide both sides of the equation by 6 like this: To divide y by 1 The y just gets copied along in the numerator. The answer is y 6y ÷ 6 = y To divide 16-2x by 6 divide each term in 16-2x by 6 term by term. 16 ÷ 6 = To divide x by 1 The x just gets copied along in the numerator. -2x ÷ 6 = The solution to your equation is: y = Now, plug the earlier result, x=11/4-5/4y, in for x everywhere it occurs in y=8/3-1/3x. This gives y=8/3-1/3(11/4-5/4y). Now all we have to do is solve this for y,to have our first solution. 8/3 evaluates to 1/3 evaluates to 11/4 evaluates to 5/4 evaluates to Multiply y and Multiply y and 1 The y just gets copied along. The answer is y y 5/4 y evaluates to 11/4-5/4 y evaluates to Multiply by we multiply by each term in term by term. This is the distributive property of multiplication. Multiply and 1 × = Multiply and Multiply 1 and y The y just gets copied along. y × = 1/3 (11/4-5/4 y) evaluates to - = The answer is 8/3-1/3 (11/4-5/4 y) evaluates to Move the to the left hand side by subtracting from both sides, like this: From the left hand side: y - = The answer is From the right hand side: - = 0 The answer is Now, the equation reads: = To isolate the y, we have to divide both sides of the equation by theother variables around the y on the left side of the equation. The last step is to divide both sides of the equation by like this: To divide y by 1 The y just gets copied along in the numerator. The answer is y ÷ = y ÷ = 3 The solution to your equation is: y = 3 Lastly, to find the solution for x, we plug this answer for y into the earlier result that x=11/4-5/4y. This gives x=11/4-5/4(3). Now, simplify this. 11/4 evaluates to 5/4 evaluates to Multiply and 3 1 5/4 (3) evaluates to 11/4-5/4 (3) evaluates to -1 x= -1 So, the solutions to your equations are: x= -1 and y= 3 The answer is x The answer is y
4x+5y=11 2x+6y=16
2x=16-6y x=8-3y
4(8-3y)+5y=11 32-12y+5y=11 -7y=-21 y=3
4x+5(3)=11 4x+15=11 4x=-4 x=-1 (-1,3)
The solution to the system of equations 4 x + 5 y = 11 and 2 x + 6 y = 16 is x = − 1 and y = 3 . This was found using the elimination method, where we manipulated the equations to eliminate one variable and then solved for the other. Substituting back verifies the solution.
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