Question

7x - 3у = −12
−2x + 3y = −3

Answer 1

2y + 19 over 7

Explanation:

Steps Using Substitution

7x−3у=−12−2x+3y=−3

Consider the first equation. Add 2x to both sides.

7x−3у+2x=−12+3y

Combine 7x and 2x to get 9x.

9x−3у=−12+3y

Subtract 3y from both sides.

9x−3у−3y=−12

Add 3у to both sides.

9x−3y=−12+3у

Consider the second equation. Add 12 to both sides.

−2x+3y=−3+12

Add −3 and 12 to get 9.

−2x+3y=9

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.

9x−3y=3у−12,−2x+3y=9

Choose one of the equations and solve it for x by isolating x on the left hand side of the equal sign.

9x−3y=3у−12

Add 3y to both sides of the equation.

9x=3y+3у−12

Divide both sides by 9.

x=1 over 9​(3y+3у−12)

Multiply 91​ times −12+3y+3у.

x=1 over 3​y+3у−4​

Substitute 3−4+y+у​ for x in the other equation, −2x+3y=9.

−2(31​y+3у−4​)+3y=9

Multiply −2 times 3−4+y+у​.

−32​y+38−2у​+3y=9

Add −2y over 3​ to 3y.

7 over 3​y+38−2у​=9

Subtract 8−2у​ over 3 from both sides of the equation.

37​y=32у+19​

Divide both sides of the equation by 37​, which is the same as multiplying both sides by the reciprocal of the fraction.

y=72у+19​

Substitute 719+2у​ for y in x=31​y+3у−4​. Because the resulting equation contains only one variable, you can solve for x directly.

x=31​×(72у+19​)+3у−4​

Multiply 31​ times 719+2у​.

x=212у+19​+3у−4​

Add 3−4+у​ to 2119+2у​.

x=73у−3​

is now solved.

y=72у+19​